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Hecke polynomials of weight 2 newforms
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Polynomials
label
$p$ 
$\chi_{f,p}(x)$
23.2.a.a
2:
x^2 + x - 1
23.2.a.a
3:
x^2 - 5
23.2.a.a
5:
x^2 + 2*x - 4
23.2.a.a
7:
x^2 - 2*x - 4
23.2.a.a
11:
x^2 + 6*x + 4
23.2.a.a
17:
x^2 - 6*x + 4
23.2.a.a
31:
x^2 - 45
23.2.a.a
37:
x^2 - 2*x - 4
23.2.a.a
41:
x^2 - 2*x - 19
23.2.a.a
47:
x^2 - 5
23.2.a.a
53:
x^2 + 8*x - 4
23.2.a.a
59:
x^2 - 4*x - 16
29.2.a.a
2:
x^2 + 2*x - 1
29.2.a.a
3:
x^2 - 2*x - 1
29.2.a.a
7:
x^2 - 8
29.2.a.a
11:
x^2 - 2*x - 1
29.2.a.a
13:
x^2 + 2*x - 7
29.2.a.a
17:
x^2 + 4*x - 4
29.2.a.a
23:
x^2 + 4*x - 28
29.2.a.a
31:
x^2 - 6*x - 41
29.2.a.a
41:
x^2 - 8*x - 56
29.2.a.a
43:
x^2 - 10*x + 23
29.2.a.a
47:
x^2 - 2*x - 17
29.2.a.a
53:
x^2 - 2*x - 71
29.2.a.a
59:
x^2 - 4*x - 28
31.2.a.a
2:
x^2 - x - 1
31.2.a.a
3:
x^2 + 2*x - 4
31.2.a.a
7:
x^2 + 4*x - 1
31.2.a.a
13:
x^2 + 2*x - 4
31.2.a.a
17:
x^2 - 6*x + 4
31.2.a.a
19:
x^2 - 5
31.2.a.a
23:
x^2 + 2*x - 44
31.2.a.a
29:
x^2 - 10*x + 20
31.2.a.a
43:
x^2 + 2*x - 4
31.2.a.a
47:
x^2 + 4*x - 16
31.2.a.a
53:
x^2 + 12*x + 16
31.2.a.a
59:
x^2 - 5
35.2.a.b
2:
x^2 + x - 4
35.2.a.b
3:
x^2 + x - 4
35.2.a.b
11:
x^2 - x - 4
35.2.a.b
13:
x^2 - 5*x + 2
35.2.a.b
17:
x^2 + 5*x + 2
35.2.a.b
19:
x^2 + 6*x - 8
35.2.a.b
23:
x^2 + 2*x - 16
35.2.a.b
29:
x^2 - x - 38
35.2.a.b
41:
x^2 - 2*x - 16
35.2.a.b
43:
x^2 - 10*x + 8
35.2.a.b
47:
x^2 + 5*x - 32
35.2.a.b
53:
x^2 + 2*x - 16
39.2.a.b
2:
x^2 + 2*x - 1
39.2.a.b
5:
x^2 - 8
39.2.a.b
7:
x^2 - 8
39.2.a.b
17:
x^2 - 4*x - 28
39.2.a.b
19:
x^2 - 8
39.2.a.b
31:
x^2 + 8*x + 8
39.2.a.b
37:
x^2 + 4*x - 28
39.2.a.b
41:
x^2 - 16*x + 56
39.2.a.b
43:
x^2 - 8*x - 16
39.2.a.b
47:
x^2 + 12*x + 4
39.2.a.b
59:
x^2 - 4*x - 28
41.2.a.a
2:
x^3 + x^2 - 5*x - 1
41.2.a.a
3:
x^3 - 4*x + 2
41.2.a.a
5:
x^3 + 2*x^2 - 4*x - 4
41.2.a.a
7:
x^3 - 6*x^2 + 8*x - 2
41.2.a.a
11:
x^3 - 2*x^2 - 20*x + 50
41.2.a.a
13:
x^3 + 2*x^2 - 12*x - 8
41.2.a.a
19:
x^3 - 4*x^2 - 16*x - 10
41.2.a.a
23:
x^3 - 4*x^2 - 32*x - 32
41.2.a.a
29:
x^3 + 6*x^2 - 4*x - 40
41.2.a.a
31:
x^3 - 16*x^2 + 64*x - 32
41.2.a.a
37:
x^3 + 6*x^2 - 36*x - 108
41.2.a.a
43:
x^3 + 4*x^2 - 8*x - 16
41.2.a.a
47:
x^3 - 120*x - 502
41.2.a.a
53:
x^3 - 6*x^2 - 4*x + 8
41.2.a.a
59:
x^3 + 8*x^2 - 16*x - 160
43.2.a.b
2:
x^2 - 2
43.2.a.b
3:
x^2 - 2
43.2.a.b
5:
x^2 - 4*x + 2
43.2.a.b
7:
x^2 + 4*x + 2
43.2.a.b
11:
x^2 + 2*x - 7
43.2.a.b
13:
x^2 - 2*x - 7
43.2.a.b
17:
x^2 - 10*x + 17
43.2.a.b
19:
x^2 + 4*x - 4
43.2.a.b
23:
x^2 - 2*x - 31
43.2.a.b
29:
x^2 - 18
43.2.a.b
37:
x^2 - 72
43.2.a.b
41:
x^2 + 2*x - 7
43.2.a.b
53:
x^2 - 22*x + 113
43.2.a.b
59:
x^2 + 4*x - 4
47.2.a.a
2:
x^4 - x^3 - 5*x^2 + 5*x - 1
47.2.a.a
3:
x^4 - 7*x^2 + 4*x + 1
47.2.a.a
5:
x^4 + 2*x^3 - 16*x^2 - 16*x + 48
47.2.a.a
7:
x^4 - 4*x^3 - 7*x^2 + 44*x - 43
47.2.a.a
11:
x^4 + 6*x^3 - 4*x^2 - 56*x - 48
47.2.a.a
13:
x^4 - 8*x^3 + 56*x + 48
47.2.a.a
17:
x^4 - 6*x^3 - 21*x^2 + 74*x + 141
47.2.a.a
19:
x^4 - 16*x^2 - 8*x + 16
47.2.a.a
23:
x^4 + 6*x^3 - 20*x^2 - 40*x - 16
47.2.a.a
29:
x^4 + 10*x^3 + 20*x^2 - 8*x - 16
47.2.a.a
31:
x^4 + 8*x^3 - 56*x + 48
47.2.a.a
37:
x^4 - 10*x^3 + 15*x^2 + 34*x + 9
47.2.a.a
41:
x^4 - 6*x^3 - 8*x^2 + 32*x - 16
47.2.a.a
43:
x^4 - 2*x^3 - 80*x^2 - 112*x + 432
47.2.a.a
53:
x^4 + 6*x^3 - 101*x^2 - 314*x + 2429
47.2.a.a
59:
x^4 - 4*x^3 - 115*x^2 + 704*x - 519
51.2.a.b
2:
x^2 + x - 4
51.2.a.b
5:
x^2 - 3*x - 2
51.2.a.b
11:
x^2 + x - 4
51.2.a.b
13:
x^2 - 5*x + 2
51.2.a.b
19:
x^2 - 3*x - 36
51.2.a.b
23:
x^2 + 9*x + 16
51.2.a.b
29:
x^2 - 68
51.2.a.b
31:
x^2 + 2*x - 16
51.2.a.b
37:
x^2 + 2*x - 16
51.2.a.b
41:
x^2 + 3*x - 2
51.2.a.b
43:
x^2 + 3*x - 36
51.2.a.b
47:
x^2 + 14*x + 32
51.2.a.b
53:
x^2 - 8*x - 52
51.2.a.b
59:
x^2 - 6*x - 8
53.2.a.b
2:
x^3 + x^2 - 3*x - 1
53.2.a.b
3:
x^3 - 3*x^2 - x + 1
53.2.a.b
5:
x^3 + 2*x^2 - 4*x - 4
53.2.a.b
7:
x^3 - 4*x^2 + 4
53.2.a.b
11:
x^3 + 4*x^2 - 4*x - 20
53.2.a.b
17:
x^3 + 5*x^2 - 5*x - 17
53.2.a.b
19:
x^3 - 11*x^2 + 37*x - 37
53.2.a.b
23:
x^3 - 3*x^2 - 31*x - 29
53.2.a.b
29:
x^3 + 5*x^2 - 37*x - 61
53.2.a.b
31:
x^3 + 2*x^2 - 76*x + 116
53.2.a.b
37:
x^3 + 5*x^2 - 89*x - 353
53.2.a.b
41:
x^3 + 10*x^2 + 20*x - 8
53.2.a.b
43:
x^3 - 18*x^2 + 24*x + 556
53.2.a.b
47:
x^3 + 10*x^2 - 4*x - 8
53.2.a.b
59:
x^3 - 2*x^2 - 60*x + 200
55.2.a.b
2:
x^2 - 2*x - 1
55.2.a.b
3:
x^2 - 8
55.2.a.b
13:
x^2 + 8*x + 8
55.2.a.b
17:
x^2 - 8*x + 8
55.2.a.b
23:
x^2 - 8
55.2.a.b
29:
x^2 - 4*x - 28
55.2.a.b
37:
x^2 + 4*x - 28
55.2.a.b
47:
x^2 - 8
55.2.a.b
53:
x^2 - 12*x + 4
55.2.a.b
59:
x^2 + 8*x - 16
59.2.a.a
2:
x^5 - 9*x^3 + 2*x^2 + 16*x - 8
59.2.a.a
3:
x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 13*x - 1
59.2.a.a
5:
x^5 - 2*x^4 - 14*x^3 + 23*x^2 + 19*x + 1
59.2.a.a
7:
x^5 - 2*x^4 - 16*x^3 + 43*x^2 + 13*x - 71
59.2.a.a
11:
x^5 + 2*x^4 - 24*x^3 - 24*x^2 + 128*x - 64
59.2.a.a
13:
x^5 - 8*x^4 + 88*x^2 - 48*x - 224
59.2.a.a
17:
x^5 + x^4 - 45*x^3 - 81*x^2 + 224*x + 412
59.2.a.a
19:
x^5 - 6*x^4 - 28*x^3 + 217*x^2 - 167*x - 469
59.2.a.a
23:
x^5 + 8*x^4 - 88*x^2 - 112*x - 32
59.2.a.a
29:
x^5 - 14*x^4 + 10*x^3 + 389*x^2 - 485*x - 1757
59.2.a.a
31:
x^5 - 116*x^3 + 56*x^2 + 1280*x + 256
59.2.a.a
37:
x^5 - 18*x^4 + 80*x^3 + 64*x^2 - 592*x + 32
59.2.a.a
41:
x^5 + 10*x^4 - 70*x^3 - 693*x^2 - 93*x + 217
59.2.a.a
43:
x^5 + 4*x^4 - 28*x^3 - 56*x^2 + 256*x - 128
59.2.a.a
47:
x^5 + 20*x^4 + 124*x^3 + 192*x^2 - 320*x - 256
59.2.a.a
53:
x^5 + 10*x^4 - 22*x^3 - 77*x^2 + 91*x + 73
61.2.a.b
2:
x^3 - x^2 - 3*x + 1
61.2.a.b
3:
x^3 - 2*x^2 - 4*x + 4
61.2.a.b
5:
x^3 + x^2 - 9*x - 13
61.2.a.b
7:
x^3 + 3*x^2 - x - 1
61.2.a.b
11:
x^3 - 13*x^2 + 53*x - 67
61.2.a.b
13:
x^3 + 9*x^2 + 11*x - 37
61.2.a.b
17:
x^3 + 2*x^2 - 8*x + 4
61.2.a.b
19:
x^3 - 48*x - 20
61.2.a.b
23:
x^3 - 5*x^2 + 5*x + 1
61.2.a.b
29:
x^3 - 4*x^2 - 4*x + 20
61.2.a.b
31:
x^3 + 2*x^2 - 76*x + 116
61.2.a.b
37:
x^3 + 6*x^2 - 36*x - 108
61.2.a.b
41:
x^3 - 3*x^2 - 61*x + 191
61.2.a.b
43:
x^3 + 14*x^2 + 56*x + 68
61.2.a.b
47:
x^3 + 4*x^2 - 88*x + 16
61.2.a.b
53:
x^3 + 2*x^2 - 12*x - 8
61.2.a.b
59:
x^3 - 29*x^2 + 231*x - 325
62.2.a.b
3:
x^2 - 2*x - 2
62.2.a.b
5:
x^2 - 12
62.2.a.b
11:
x^2 + 6*x + 6
62.2.a.b
13:
x^2 + 2*x - 26
62.2.a.b
17:
x^2 - 12
62.2.a.b
29:
x^2 + 6*x - 18
62.2.a.b
37:
x^2 - 10*x - 2
62.2.a.b
41:
x^2 - 12*x + 24
62.2.a.b
43:
x^2 + 2*x - 26
62.2.a.b
53:
x^2 - 6*x + 6
62.2.a.b
59:
x^2 + 12*x + 24
63.2.a.b
2:
x^2 - 3
63.2.a.b
5:
x^2 - 12
63.2.a.b
11:
x^2 - 12
63.2.a.b
17:
x^2 - 12
63.2.a.b
23:
x^2 - 12
63.2.a.b
41:
x^2 - 108
63.2.a.b
47:
x^2 - 48
63.2.a.b
53:
x^2 - 48
63.2.a.b
59:
x^2 - 48
65.2.a.b
2:
x^2 + 2*x - 1
65.2.a.b
3:
x^2 - 2
65.2.a.b
7:
x^2 - 4*x - 4
65.2.a.b
11:
x^2 - 4*x + 2
65.2.a.b
17:
x^2 + 4*x - 4
65.2.a.b
19:
x^2 - 4*x + 2
65.2.a.b
23:
x^2 - 2
65.2.a.b
29:
x^2 - 32
65.2.a.b
31:
x^2 - 12*x + 18
65.2.a.b
37:
x^2 - 72
65.2.a.b
41:
x^2 + 12*x + 28
65.2.a.b
43:
x^2 + 8*x - 34
65.2.a.b
47:
x^2 + 4*x - 4
65.2.a.b
53:
x^2 + 12*x - 36
65.2.a.b
59:
x^2 - 12*x + 18
65.2.a.c
2:
x^2 - 3
65.2.a.c
3:
x^2 - 2*x - 2
65.2.a.c
11:
x^2 + 6*x + 6
65.2.a.c
17:
x^2 - 12
65.2.a.c
19:
x^2 + 2*x - 26
65.2.a.c
23:
x^2 - 6*x + 6
65.2.a.c
29:
x^2 + 12*x + 24
65.2.a.c
31:
x^2 - 10*x - 2
65.2.a.c
41:
x^2 - 12
65.2.a.c
43:
x^2 - 10*x - 2
65.2.a.c
53:
x^2 - 108
65.2.a.c
59:
x^2 + 6*x - 138
67.2.a.b
2:
x^2 + 3*x + 1
67.2.a.b
3:
x^2 + 3*x + 1
67.2.a.b
7:
x^2 + x - 11
67.2.a.b
11:
x^2 - 5
67.2.a.b
13:
x^2 + 7*x + 1
67.2.a.b
17:
x^2 + 6*x + 4
67.2.a.b
19:
x^2 - x - 11
67.2.a.b
23:
x^2 - 6*x - 11
67.2.a.b
29:
x^2 + 6*x - 11
67.2.a.b
37:
x^2 + x - 11
67.2.a.b
41:
x^2 + 3*x + 1
67.2.a.b
43:
x^2 - 3*x - 9
67.2.a.b
47:
x^2 + 15*x + 55
67.2.a.c
2:
x^2 + x - 1
67.2.a.c
3:
x^2 - x - 1
67.2.a.c
5:
x^2 - 4*x - 1
67.2.a.c
7:
x^2 - x - 1
67.2.a.c
13:
x^2 + x - 1
67.2.a.c
17:
x^2 - 6*x + 4
67.2.a.c
19:
x^2 + 11*x + 29
67.2.a.c
23:
x^2 + 2*x - 19
67.2.a.c
29:
x^2 - 10*x + 5
67.2.a.c
31:
x^2 - 45
67.2.a.c
37:
x^2 - 3*x + 1
67.2.a.c
41:
x^2 - 5*x - 25
67.2.a.c
43:
x^2 + 9*x - 11
67.2.a.c
47:
x^2 + 7*x + 11
67.2.a.c
53:
x^2 - 45
68.2.a.a
3:
x^2 - 2*x - 2
68.2.a.a
5:
x^2 - 12
68.2.a.a
7:
x^2 + 2*x - 2
68.2.a.a
11:
x^2 + 6*x + 6
68.2.a.a
13:
x^2 - 4*x - 8
68.2.a.a
19:
x^2 - 4*x - 8
68.2.a.a
23:
x^2 + 6*x + 6
68.2.a.a
29:
x^2 - 12
68.2.a.a
31:
x^2 + 2*x - 26
68.2.a.a
37:
x^2 - 16*x + 52
68.2.a.a
43:
x^2 - 4*x - 104
68.2.a.a
47:
x^2 - 48
68.2.a.a
53:
x^2 - 12*x - 12
68.2.a.a
59:
x^2 - 12*x + 24
69.2.a.b
2:
x^2 - 5
69.2.a.b
5:
x^2 + 2*x - 4
69.2.a.b
7:
x^2 - 2*x - 4
69.2.a.b
13:
x^2 - 20
69.2.a.b
17:
x^2 + 10*x + 20
69.2.a.b
19:
x^2 - 10*x + 20
69.2.a.b
29:
x^2 - 20
69.2.a.b
31:
x^2 + 4*x - 16
69.2.a.b
37:
x^2 - 20
69.2.a.b
41:
x^2 + 4*x - 76
69.2.a.b
43:
x^2 - 2*x - 44
69.2.a.b
53:
x^2 + 6*x + 4
69.2.a.b
59:
x^2 - 8*x - 64
71.2.a.a
2:
x^3 + x^2 - 4*x - 3
71.2.a.a
3:
x^3 - x^2 - 4*x + 3
71.2.a.a
5:
x^3 - 5*x^2 - 2*x + 25
71.2.a.a
7:
x^3 - 2*x^2 - 16*x + 24
71.2.a.a
11:
x^3 - 20*x + 24
71.2.a.a
13:
x^3 + 6*x^2 - 8*x - 56
71.2.a.a
17:
x^3 + 2*x^2 - 32*x - 24
71.2.a.a
19:
x^3 - x^2 - 20*x - 25
71.2.a.a
29:
x^3 - 11*x^2 + 14*x + 71
71.2.a.a
37:
x^3 + 15*x^2 + 70*x + 97
71.2.a.a
41:
x^3 + 2*x^2 - 68*x + 56
71.2.a.a
43:
x^3 - 13*x^2 + 48*x - 45
71.2.a.a
47:
x^3 - 4*x^2 - 28*x + 40
71.2.a.a
53:
x^3 + 18*x^2 + 28*x - 456
71.2.a.a
59:
x^3 + 4*x^2 - 36*x - 152
71.2.a.b
2:
x^3 - 5*x + 3
71.2.a.b
3:
x^3 + x^2 - 8*x - 3
71.2.a.b
5:
x^3 + 3*x^2 - 2*x - 7
71.2.a.b
7:
x^3 - 2*x^2 - 16*x + 24
71.2.a.b
11:
x^3 + 2*x^2 - 16*x - 24
71.2.a.b
17:
x^3 - 2*x^2 - 16*x + 24
71.2.a.b
19:
x^3 - 11*x^2 + 36*x - 35
71.2.a.b
23:
x^3 - 8*x^2 - 12*x + 72
71.2.a.b
29:
x^3 + 5*x^2 - 2*x - 25
71.2.a.b
31:
x^3 + 6*x^2 - 8*x - 56
71.2.a.b
37:
x^3 - 9*x^2 - 26*x + 37
71.2.a.b
41:
x^3 - 14*x^2 + 48*x - 8
71.2.a.b
43:
x^3 + 17*x^2 + 72*x + 81
71.2.a.b
47:
x^3 + 10*x^2 - 72
71.2.a.b
53:
x^3 - 20*x - 24
71.2.a.b
59:
x^3 + 22*x^2 + 144*x + 280
73.2.a.b
2:
x^2 + 3*x + 1
73.2.a.b
3:
x^2 + 3*x + 1
73.2.a.b
5:
x^2 + 3*x + 1
73.2.a.b
11:
x^2 + 3*x + 1
73.2.a.b
13:
x^2 - x - 11
73.2.a.b
17:
x^2 - 45
73.2.a.b
23:
x^2 + 15*x + 55
73.2.a.b
29:
x^2 - 6*x - 11
73.2.a.b
31:
x^2 - 2*x - 44
73.2.a.b
37:
x^2 + 4*x - 41
73.2.a.b
41:
x^2 - 20
73.2.a.b
47:
x^2 + 6*x - 11
73.2.a.b
53:
x^2 - 6*x - 71
73.2.a.b
59:
x^2 + 12*x + 16
73.2.a.c
2:
x^2 - x - 3
73.2.a.c
3:
x^2 - x - 3
73.2.a.c
5:
x^2 + x - 3
73.2.a.c
11:
x^2 - 7*x + 9
73.2.a.c
13:
x^2 + x - 3
73.2.a.c
17:
x^2 + 4*x - 9
73.2.a.c
23:
x^2 - 13*x + 39
73.2.a.c
29:
x^2 - 2*x - 51
73.2.a.c
31:
x^2 - 6*x - 4
73.2.a.c
37:
x^2 - 8*x + 3
73.2.a.c
43:
x^2 - 6*x - 43
73.2.a.c
53:
x^2 + 2*x - 51
74.2.a.a
3:
x^2 - 3*x - 1
74.2.a.a
5:
x^2 + x - 3
74.2.a.a
7:
x^2 - 2*x - 12
74.2.a.a
11:
x^2 + x - 3
74.2.a.a
13:
x^2 + x - 3
74.2.a.a
23:
x^2 + 3*x - 27
74.2.a.a
29:
x^2 - 3*x - 27
74.2.a.a
31:
x^2 - 3*x - 1
74.2.a.a
41:
x^2 - 9*x - 9
74.2.a.a
43:
x^2 + 6*x - 4
74.2.a.a
47:
x^2 - 2*x - 12
74.2.a.a
59:
x^2 - 14*x + 36
74.2.a.b
3:
x^2 + x - 1
74.2.a.b
5:
x^2 - x - 11
74.2.a.b
7:
x^2 + 2*x - 4
74.2.a.b
11:
x^2 + 5*x + 5
74.2.a.b
13:
x^2 - x - 11
74.2.a.b
17:
x^2 - 20
74.2.a.b
19:
x^2 - 20
74.2.a.b
23:
x^2 + x - 11
74.2.a.b
29:
x^2 + 3*x - 59
74.2.a.b
31:
x^2 - 17*x + 71
74.2.a.b
41:
x^2 - 17*x + 71
74.2.a.b
43:
x^2 + 6*x + 4
74.2.a.b
47:
x^2 - 2*x - 4
74.2.a.b
53:
x^2 + 8*x - 4
74.2.a.b
59:
x^2 + 14*x + 44
77.2.a.d
2:
x^2 - 5
77.2.a.d
3:
x^2 - 2*x - 4
77.2.a.d
13:
x^2 - 2*x - 4
77.2.a.d
17:
x^2 + 2*x - 4
77.2.a.d
19:
x^2 - 4*x - 16
77.2.a.d
23:
x^2 + 4*x - 16
77.2.a.d
29:
x^2 - 8*x - 4
77.2.a.d
31:
x^2 + 10*x + 20
77.2.a.d
37:
x^2 + 8*x - 4
77.2.a.d
41:
x^2 + 18*x + 76
77.2.a.d
47:
x^2 - 10*x + 20
77.2.a.d
53:
x^2 - 8*x - 4
77.2.a.d
59:
x^2 - 2*x - 4
79.2.a.b
2:
x^5 - 6*x^3 + 8*x - 1
79.2.a.b
3:
x^5 - x^4 - 12*x^3 + 8*x^2 + 24*x - 16
79.2.a.b
5:
x^5 - 7*x^4 + 9*x^3 + 27*x^2 - 65*x + 31
79.2.a.b
7:
x^5 + 5*x^4 - 6*x^3 - 52*x^2 - 56*x - 16
79.2.a.b
11:
x^5 - 2*x^4 - 35*x^3 + 34*x^2 + 185*x + 106
79.2.a.b
13:
x^5 + 3*x^4 - 23*x^3 - 123*x^2 - 197*x - 103
79.2.a.b
17:
x^5 - 10*x^4 + 16*x^3 + 88*x^2 - 224*x + 32
79.2.a.b
19:
x^5 + 4*x^4 - 47*x^3 - 124*x^2 + 541*x + 488
79.2.a.b
23:
x^5 - 2*x^4 - 43*x^3 + 106*x^2 + 177*x - 142
79.2.a.b
29:
x^5 - 6*x^4 - 52*x^3 + 392*x^2 - 496*x - 32
79.2.a.b
31:
x^5 - 2*x^4 - 63*x^3 + 6*x^2 + 397*x + 314
79.2.a.b
37:
x^5 - 84*x^3 - 64*x^2 + 1264*x + 2272
79.2.a.b
41:
x^5 - 30*x^4 + 336*x^3 - 1752*x^2 + 4256*x - 3872
79.2.a.b
43:
x^5 + 14*x^4 + 44*x^3 - 120*x^2 - 688*x - 704
79.2.a.b
47:
x^5 - 5*x^4 - 136*x^3 + 536*x^2 + 4176*x - 13456
79.2.a.b
53:
x^5 - 2*x^4 - 136*x^3 - 240*x^2 + 3792*x + 12352
79.2.a.b
59:
x^5 - 5*x^4 - 70*x^3 + 368*x^2 + 864*x - 4624
81.2.a.a
2:
x^2 - 3
81.2.a.a
5:
x^2 - 3
81.2.a.a
11:
x^2 - 12
81.2.a.a
17:
x^2 - 27
81.2.a.a
23:
x^2 - 12
81.2.a.a
29:
x^2 - 3
81.2.a.a
41:
x^2 - 48
81.2.a.a
47:
x^2 - 48
81.2.a.a
59:
x^2 - 192
82.2.a.b
3:
x^2 - 2
82.2.a.b
5:
x^2 - 8
82.2.a.b
7:
x^2 + 4*x + 2
82.2.a.b
11:
x^2 - 18
82.2.a.b
17:
x^2 - 4*x - 28
82.2.a.b
19:
x^2 + 8*x + 14
82.2.a.b
23:
x^2 - 8*x + 8
82.2.a.b
29:
x^2 - 8*x - 16
82.2.a.b
31:
x^2 + 8*x + 8
82.2.a.b
37:
x^2 - 72
82.2.a.b
43:
x^2 - 8*x - 16
82.2.a.b
47:
x^2 + 4*x - 46
82.2.a.b
59:
x^2 + 8*x + 8
83.2.a.b
2:
x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8
83.2.a.b
3:
x^6 - x^5 - 10*x^4 + 5*x^3 + 30*x^2 - 4*x - 25
83.2.a.b
5:
x^6 - 2*x^5 - 20*x^4 + 28*x^3 + 104*x^2 - 64*x - 160
83.2.a.b
7:
x^6 - 3*x^5 - 22*x^4 + 55*x^3 + 154*x^2 - 228*x - 409
83.2.a.b
11:
x^6 + 3*x^5 - 26*x^4 - 83*x^3 + 66*x^2 + 156*x - 113
83.2.a.b
13:
x^6 - 14*x^5 + 44*x^4 + 108*x^3 - 488*x^2 - 288*x + 992
83.2.a.b
17:
x^6 + 5*x^5 - 20*x^4 - 77*x^3 + 162*x^2 + 188*x - 275
83.2.a.b
19:
x^6 + 4*x^5 - 68*x^4 - 300*x^3 + 976*x^2 + 5648*x + 6176
83.2.a.b
23:
x^6 + 5*x^5 - 61*x^4 - 377*x^3 + 608*x^2 + 7024*x + 10912
83.2.a.b
29:
x^6 + x^5 - 88*x^4 - 181*x^3 + 578*x^2 - 192*x - 55
83.2.a.b
31:
x^6 - 3*x^5 - 66*x^4 - 93*x^3 + 390*x^2 + 608*x - 313
83.2.a.b
37:
x^6 - 39*x^5 + 576*x^4 - 3785*x^3 + 7934*x^2 + 22268*x - 91499
83.2.a.b
41:
x^6 + x^5 - 47*x^4 - x^3 + 482*x^2 - 516*x - 248
83.2.a.b
43:
x^6 + 8*x^5 - 44*x^4 - 456*x^3 - 192*x^2 + 4224*x + 6400
83.2.a.b
47:
x^6 + 12*x^5 - 96*x^4 - 1812*x^3 - 6648*x^2 + 992*x + 25952
83.2.a.b
53:
x^6 - 14*x^5 - 64*x^4 + 1064*x^3 + 448*x^2 - 10048*x - 64
83.2.a.b
59:
x^6 + 17*x^5 + 10*x^4 - 493*x^3 - 1018*x^2 + 1768*x + 3527
85.2.a.b
2:
x^2 + 2*x - 1
85.2.a.b
3:
x^2 + 4*x + 2
85.2.a.b
7:
x^2 + 4*x + 2
85.2.a.b
11:
x^2 + 8*x + 14
85.2.a.b
13:
x^2 - 8
85.2.a.b
19:
x^2 - 8
85.2.a.b
23:
x^2 + 4*x + 2
85.2.a.b
29:
x^2 + 4*x - 4
85.2.a.b
31:
x^2 - 18
85.2.a.b
37:
x^2 + 4*x - 68
85.2.a.b
41:
x^2 - 4*x - 68
85.2.a.b
43:
x^2 - 4*x - 28
85.2.a.b
47:
x^2 + 4*x - 4
85.2.a.b
53:
x^2 - 12*x + 4
85.2.a.b
59:
x^2 + 24*x + 136
85.2.a.c
2:
x^2 - 3
85.2.a.c
3:
x^2 - 2*x - 2
85.2.a.c
7:
x^2 + 2*x - 2
85.2.a.c
11:
x^2 - 6*x + 6
85.2.a.c
19:
x^2 - 4*x - 8
85.2.a.c
23:
x^2 + 6*x - 18
85.2.a.c
29:
x^2 - 12
85.2.a.c
31:
x^2 - 10*x + 22
85.2.a.c
37:
x^2 + 8*x + 4
85.2.a.c
41:
x^2 - 12
85.2.a.c
43:
x^2 + 8*x + 4
85.2.a.c
47:
x^2 - 12*x - 12
85.2.a.c
59:
x^2 - 12*x + 24
86.2.a.a
3:
x^2 + x - 5
86.2.a.a
5:
x^2 - 3*x - 3
86.2.a.a
17:
x^2 + 9*x + 15
86.2.a.a
19:
x^2 - x - 47
86.2.a.a
23:
x^2 + 9*x + 15
86.2.a.a
29:
x^2 - 3*x - 3
86.2.a.a
31:
x^2 - x - 47
86.2.a.a
37:
x^2 - x - 47
86.2.a.a
41:
x^2 - 3*x - 45
86.2.a.a
47:
x^2 + 9*x - 27
86.2.a.a
53:
x^2 - 6*x - 12
86.2.a.b
3:
x^2 - x - 1
86.2.a.b
5:
x^2 + 3*x + 1
86.2.a.b
7:
x^2 - 20
86.2.a.b
11:
x^2 + 4*x - 16
86.2.a.b
13:
x^2 - 20
86.2.a.b
17:
x^2 + x - 1
86.2.a.b
19:
x^2 - 11*x + 29
86.2.a.b
23:
x^2 - 3*x - 9
86.2.a.b
29:
x^2 + 7*x + 1
86.2.a.b
31:
x^2 - 13*x + 41
86.2.a.b
37:
x^2 + 5*x + 5
86.2.a.b
41:
x^2 + 5*x - 5
86.2.a.b
47:
x^2 - 3*x - 59
86.2.a.b
53:
x^2 + 10*x + 20
86.2.a.b
59:
x^2 - 16*x + 44
87.2.a.a
2:
x^2 - x - 1
87.2.a.a
5:
x^2 - 2*x - 4
87.2.a.a
7:
x^2 + 4*x - 1
87.2.a.a
11:
x^2 - 4*x - 1
87.2.a.a
13:
x^2 + 2*x - 19
87.2.a.a
19:
x^2 + 10*x + 20
87.2.a.a
23:
x^2 + 2*x - 44
87.2.a.a
31:
x^2 + 6*x - 36
87.2.a.a
37:
x^2 - 6*x + 4
87.2.a.a
47:
x^2 + 4*x - 41
87.2.a.a
53:
x^2 - 18*x + 76
87.2.a.a
59:
x^2 - 20
87.2.a.b
2:
x^3 - 2*x^2 - 4*x + 7
87.2.a.b
5:
x^3 - 16*x + 8
87.2.a.b
7:
x^3 - 4*x^2 - x + 8
87.2.a.b
11:
x^3 + 8*x^2 + 15*x + 4
87.2.a.b
13:
x^3 - 4*x^2 - 7*x + 26
87.2.a.b
17:
x^3 - 4*x^2 - 27*x + 94
87.2.a.b
19:
x^3 + 2*x^2 - 20*x + 16
87.2.a.b
23:
x^3 - 6*x^2 - 4*x + 32
87.2.a.b
31:
x^3 - 6*x^2 - 4*x + 32
87.2.a.b
37:
x^3 - 8*x^2 + 8
87.2.a.b
41:
x^3 + 2*x^2 - 100*x + 56
87.2.a.b
43:
x^3 + 4*x^2 - 96*x - 256
87.2.a.b
47:
x^3 + 12*x^2 - 9*x - 216
87.2.a.b
53:
x^3 - 8*x^2 - 104*x + 248
87.2.a.b
59:
x^3 + 20*x^2 + 108*x + 112
88.2.a.b
3:
x^2 - x - 4
88.2.a.b
5:
x^2 - 3*x - 2
88.2.a.b
7:
x^2 + 2*x - 16
88.2.a.b
13:
x^2 + 2*x - 16
88.2.a.b
23:
x^2 - 9*x + 16
88.2.a.b
29:
x^2 + 2*x - 16
88.2.a.b
31:
x^2 + 7*x + 8
88.2.a.b
37:
x^2 + 11*x + 26
88.2.a.b
41:
x^2 - 6*x - 8
88.2.a.b
43:
x^2 + 6*x - 8
88.2.a.b
53:
x^2 - 8*x - 52
88.2.a.b
59:
x^2 + 5*x - 100
89.2.a.c
2:
x^5 + x^4 - 10*x^3 - 10*x^2 + 21*x + 17
89.2.a.c
3:
x^5 + 3*x^4 - 4*x^3 - 16*x^2 - 9*x - 1
89.2.a.c
5:
x^5 + x^4 - 14*x^3 - 14*x^2 + 29*x + 13
89.2.a.c
7:
x^5 - 8*x^4 + 10*x^3 + 36*x^2 - 68*x + 28
89.2.a.c
11:
x^5 - 6*x^4 - 20*x^3 + 112*x^2 + 80*x - 112
89.2.a.c
13:
x^5 - 28*x^3 - 56*x^2 + 16
89.2.a.c
17:
x^5 + 13*x^4 + 34*x^3 - 154*x^2 - 791*x - 883
89.2.a.c
19:
x^5 - 13*x^4 + 42*x^3 + 42*x^2 - 297*x + 199
89.2.a.c
23:
x^5 - x^4 - 62*x^3 + 150*x^2 + 631*x - 1657
89.2.a.c
29:
x^5 - 2*x^4 - 72*x^3 + 312*x^2 - 48*x - 784
89.2.a.c
31:
x^5 - 19*x^4 + 102*x^3 - 114*x^2 + 13*x + 7
89.2.a.c
37:
x^5 + 14*x^4 + 8*x^3 - 336*x^2 + 80*x + 1120
89.2.a.c
41:
x^5 + 2*x^4 - 60*x^3 - 24*x^2 + 800*x - 1072
89.2.a.c
43:
x^5 - x^4 - 68*x^3 - 56*x^2 + 877*x + 1573
89.2.a.c
47:
x^5 + 4*x^4 - 44*x^3 + 32*x^2 + 112*x - 16
89.2.a.c
53:
x^5 + 11*x^4 - 6*x^3 - 342*x^2 - 547*x + 1319
89.2.a.c
59:
x^5 - 118*x^3 + 784*x^2 - 1900*x + 1580
91.2.a.c
2:
x^2 - 2
91.2.a.c
3:
x^2 - 2
91.2.a.c
5:
x^2 - 6*x + 7
91.2.a.c
11:
x^2 - 18
91.2.a.c
17:
x^2 - 2
91.2.a.c
19:
x^2 + 6*x - 9
91.2.a.c
23:
x^2 + 6*x + 1
91.2.a.c
29:
x^2 - 6*x + 1
91.2.a.c
31:
x^2 + 2*x - 17
91.2.a.c
37:
x^2 + 4*x - 14
91.2.a.c
41:
x^2 - 12*x + 28
91.2.a.c
47:
x^2 - 6*x + 7
91.2.a.c
53:
x^2 + 6*x + 1
91.2.a.c
59:
x^2 - 12*x + 4
91.2.a.d
2:
x^3 - x^2 - 4*x + 2
91.2.a.d
3:
x^3 + 2*x^2 - 6*x - 8
91.2.a.d
5:
x^3 - 2*x^2 - 3*x + 2
91.2.a.d
11:
x^3 - 2*x^2 - 6*x + 8
91.2.a.d
17:
x^3 - 4*x^2 - 10*x - 4
91.2.a.d
19:
x^3 + 4*x^2 + x - 4
91.2.a.d
23:
x^3 - 10*x^2 + x + 136
91.2.a.d
29:
x^3 - 24*x^2 + 185*x - 454
91.2.a.d
31:
x^3 + 4*x^2 - 19*x + 16
91.2.a.d
37:
x^3 - 58*x - 124
91.2.a.d
41:
x^3 - 2*x^2 - 28*x - 8
91.2.a.d
43:
x^3 - 10*x^2 - 71*x + 628
91.2.a.d
47:
x^3 + 8*x^2 - 79*x - 544
91.2.a.d
53:
x^3 - 8*x^2 - 35*x - 22
91.2.a.d
59:
x^3 + 4*x^2 - 156*x - 688
93.2.a.a
2:
x^2 + 3*x + 1
93.2.a.a
5:
x^2 + 4*x - 1
93.2.a.a
7:
x^2 + 4*x - 1
93.2.a.a
11:
x^2 + 6*x + 4
93.2.a.a
13:
x^2 + 2*x - 4
93.2.a.a
17:
x^2 + 4*x - 16
93.2.a.a
19:
x^2 + 8*x + 11
93.2.a.a
23:
x^2 - 2*x - 4
93.2.a.a
29:
x^2 - 2*x - 4
93.2.a.a
37:
x^2 - 2*x - 44
93.2.a.a
41:
x^2 - 45
93.2.a.a
43:
x^2 + 6*x - 36
93.2.a.a
47:
x^2 - 4*x - 16
93.2.a.a
53:
x^2 - 80
93.2.a.b
2:
x^3 - 4*x + 1
93.2.a.b
5:
x^3 + 2*x^2 - 5*x - 2
93.2.a.b
7:
x^3 - 4*x^2 - x + 8
93.2.a.b
11:
x^3 + 2*x^2 - 20*x + 16
93.2.a.b
13:
x^3 - 4*x^2 - 16*x + 56
93.2.a.b
17:
x^3 + 2*x^2 - 24*x - 32
93.2.a.b
19:
x^3 - 4*x^2 - 45*x + 196
93.2.a.b
23:
x^3 + 6*x^2 - 4*x - 32
93.2.a.b
29:
x^3 + 8*x^2 - 56*x - 392
93.2.a.b
37:
x^3 - 16*x + 8
93.2.a.b
41:
x^3 + 10*x^2 - 17*x - 262
93.2.a.b
43:
x^3 - 14*x^2 + 4*x + 368
93.2.a.b
47:
x^3 - 12*x^2 - 16*x + 256
93.2.a.b
53:
x^3 + 10*x^2 - 16*x - 32
93.2.a.b
59:
x^3 - 26*x^2 + 213*x - 556
94.2.a.b
3:
x^2 - 8
94.2.a.b
5:
x^2 - 4*x + 2
94.2.a.b
7:
x^2 + 4*x - 4
94.2.a.b
11:
x^2 - 8*x + 14
94.2.a.b
13:
x^2 + 4*x + 2
94.2.a.b
19:
x^2 + 8*x - 2
94.2.a.b
23:
x^2 - 8
94.2.a.b
29:
x^2 - 12*x + 18
94.2.a.b
31:
x^2 - 72
94.2.a.b
37:
x^2 - 4*x - 68
94.2.a.b
41:
x^2 + 12*x + 28
94.2.a.b
43:
x^2 + 8*x - 2
94.2.a.b
53:
x^2 - 4*x - 4
94.2.a.b
59:
x^2 + 8*x - 16
95.2.a.a
2:
x^3 - x^2 - 3*x + 1
95.2.a.a
3:
x^3 - 2*x^2 - 4*x + 4
95.2.a.a
7:
x^3 - 16*x + 16
95.2.a.a
11:
x^3 + 8*x^2 + 8*x - 16
95.2.a.a
13:
x^3 - 8*x^2 + 12*x - 4
95.2.a.a
17:
x^3 - 2*x^2 - 36*x + 104
95.2.a.a
23:
x^3 + 4*x^2 - 8*x - 16
95.2.a.a
29:
x^3 + 10*x^2 + 12*x - 40
95.2.a.a
31:
x^3 - 4*x^2 - 48*x + 64
95.2.a.a
37:
x^3 - 20*x^2 + 124*x - 244
95.2.a.a
41:
x^3 + 2*x^2 - 36*x - 104
95.2.a.a
43:
x^3 + 4*x^2 - 144*x - 592
95.2.a.a
47:
x^3 - 16*x + 16
95.2.a.a
53:
x^3 - 16*x^2 + 76*x - 92
95.2.a.a
59:
x^3 + 20*x^2 + 112*x + 160
95.2.a.b
2:
x^4 + 2*x^3 - 6*x^2 - 8*x + 9
95.2.a.b
3:
x^4 - 2*x^3 - 8*x^2 + 16*x - 4
95.2.a.b
7:
x^4 - 4*x^3 - 16*x^2 + 48*x + 32
95.2.a.b
11:
x^4 - 4*x^3 - 16*x^2 + 32*x + 48
95.2.a.b
13:
x^4 - 2*x^3 - 24*x^2 + 32*x + 20
95.2.a.b
17:
x^4 - 4*x^3 - 32*x^2 + 16*x + 48
95.2.a.b
23:
x^4 + 8*x^3 - 24*x^2 - 176*x + 288
95.2.a.b
29:
x^4 - 4*x^3 - 32*x^2 + 16*x + 48
95.2.a.b
31:
x^4 - 4*x^3 - 80*x^2 + 512*x - 640
95.2.a.b
37:
x^4 + 6*x^3 - 24*x^2 - 40*x + 4
95.2.a.b
41:
x^4 - 16*x^3 + 56*x^2 + 32*x - 240
95.2.a.b
43:
x^4 - 4*x^3 - 16*x^2 + 48*x + 32
95.2.a.b
47:
x^4 + 12*x^3 - 64*x^2 - 656*x + 1056
95.2.a.b
53:
x^4 + 10*x^3 - 184*x - 348
95.2.a.b
59:
x^4 - 64*x^2 - 224*x - 192
97.2.a.a
2:
x^3 + 4*x^2 + 3*x - 1
97.2.a.a
3:
x^3 + 4*x^2 + 3*x - 1
97.2.a.a
5:
x^3 + 3*x^2 - 4*x + 1
97.2.a.a
7:
x^3 + 7*x^2 + 14*x + 7
97.2.a.a
11:
x^3 + 7*x^2 + 14*x + 7
97.2.a.a
13:
x^3 + 2*x^2 - x - 1
97.2.a.a
17:
x^3 + 3*x^2 - 4*x - 13
97.2.a.a
19:
x^3 - 5*x^2 - 57*x + 293
97.2.a.a
23:
x^3 + 12*x^2 + 27*x - 13
97.2.a.a
29:
x^3 - x^2 - 65*x + 169
97.2.a.a
31:
x^3 + 8*x^2 + 5*x - 43
97.2.a.a
37:
x^3 + 2*x^2 - 71*x + 97
97.2.a.a
41:
x^3 - 3*x^2 - 4*x - 1
97.2.a.a
43:
x^3 - x^2 - 16*x + 29
97.2.a.a
47:
x^3 + 17*x^2 + 59*x - 13
97.2.a.a
53:
x^3 - 2*x^2 - 155*x + 659
97.2.a.a
59:
x^3 - 19*x^2 + 104*x - 169
97.2.a.b
2:
x^4 - 3*x^3 - x^2 + 6*x - 1
97.2.a.b
3:
x^4 - 5*x^2 - x + 4
97.2.a.b
5:
x^4 - x^3 - 4*x^2 + x + 2
97.2.a.b
7:
x^4 - 3*x^3 - 6*x^2 + 23*x - 16
97.2.a.b
11:
x^4 - 5*x^3 - 14*x^2 + 47*x + 92
97.2.a.b
13:
x^4 + 6*x^3 - 29*x^2 - 167*x - 122
97.2.a.b
17:
x^4 - 3*x^3 - 20*x^2 + 15*x + 74
97.2.a.b
19:
x^4 + 3*x^3 - 5*x^2 - 11*x + 4
97.2.a.b
23:
x^4 - 22*x^3 + 151*x^2 - 265*x - 368
97.2.a.b
29:
x^4 - 7*x^3 - 27*x^2 + 199*x - 254
97.2.a.b
31:
x^4 + 4*x^3 - 67*x^2 - 79*x + 592
97.2.a.b
37:
x^4 + 6*x^3 - 27*x^2 - 81*x + 162
97.2.a.b
41:
x^4 - 3*x^3 - 158*x^2 + 131*x + 5506
97.2.a.b
43:
x^4 - 9*x^3 + 20*x^2 + 9*x - 44
97.2.a.b
47:
x^4 - 19*x^3 + 99*x^2 - 161*x + 16
97.2.a.b
53:
x^4 + 4*x^3 - 75*x^2 - 123*x + 1262
97.2.a.b
59:
x^4 - x^3 - 98*x^2 + 3*x + 772
98.2.a.b
3:
x^2 - 2
98.2.a.b
5:
x^2 - 8
98.2.a.b
17:
x^2 - 2
98.2.a.b
19:
x^2 - 50
98.2.a.b
31:
x^2 - 72
98.2.a.b
41:
x^2 - 98
98.2.a.b
47:
x^2 - 8
98.2.a.b
59:
x^2 - 2
Definition
For a normalized newform $f(q)=\sum_{n\geq1}a_nq^n$ of weight $2$, trivial character and level $N$, let $K_f=\mathbb{Q}(a_n:n\geq1)$ be its coefficient field. For a prime $p$, this table gives the characteristic polynomial $\chi_{f,p}(x)$ of multiplication by the Hecke eigenvalue $a_p$ [1] on $K_f$.
Parameters
label
—   LMFDB newform label (the label has the form $N.2.a.o$ for a weight $2$ newform orbit of trivial character on $\Gamma_0(N)$, with $[K_f:\mathbb{Q}]\geq2$)
$p$
—   prime ($p$ is prime)
Formulas
(1)
If $p\nmid N$, then $T_pf=a_pf$. If $p\mid N$, the same symbol $a_p$ denotes the eigenvalue of the operator $U_p$ on $f$.
(2)
$\chi_{f,p}(x)=\prod_{\sigma:K_f\hookrightarrow\mathbb{C}} (x-\sigma(a_p))$, counted with multiplicity.
Comments
(3)
The labels are the LMFDB labels [3] for weight $2$ newform orbits with trivial character. The character orbit is a, and the final letter names the Hecke orbit at that level.
(4)
Dimension-one newforms are omitted. For such a form $K_f=\mathbb{Q}$ and $\chi_{f,p}(x)=x-a_p$ is a linear polynomial; the corresponding $a_p$ are the elliptic-curve traces in Cremona and LMFDB tables.
(5)
The table stores the characteristic polynomial on $K_f$, not the minimal polynomial of $a_p$. Its degree is $[K_f:\mathbb{Q}]$, the dimension of the newform orbit. The two polynomials agree exactly when $a_p$ generates $K_f$, and those are the rows the table keeps.
(6)
Rows where $a_p$ does not generate $K_f$ are omitted, because $\chi_{f,p}$ is then a proper power of the minimal polynomial of $a_p$ and carries nothing the generating primes do not already give. In the extreme $a_p\in\mathbb{Q}$ and $\chi_{f,p}(x)=(x-a_p)^{[K_f:\mathbb{Q}]}$: at $f=23.2.a.a$ and $p=13$ the eigenvalue is $a_{13}=3$ and the characteristic polynomial is $(x-3)^2$, which is a small integer and the degree of a field rather than a number worth looking up.
(7)
A polynomial can answer for more than one row. The $686$ entries hold $424$ distinct polynomials, of which $317$ occur once; the repetitions are small-height quadratics, $x^2-8$ and $x^2-12$ occurring $14$ times each. Some repeat within a single orbit, where two primes give conjugate eigenvalues: $a_5$ and $a_7$ of $39.2.a.b$ are both roots of $x^2-8$.
(8)
The eigenvalues are the usual Fourier coefficients $a_p$, not the analytically normalised values $a_p/\sqrt{p}$. If $p\mid N$, $a_p$ is the eigenvalue of $U_p$: it is $-w_p$ for the Atkin-Lehner sign $w_p$ when $p^2\nmid N$, and it is $0$ when $p^2\mid N$.
Programs
(P1)
Sage
import sage.rings.polynomial.laurent_polynomial_ring
from sage.modular.modform.constructor import Newforms

f = Newforms(23, 2, names='a')[0]
f.coefficient(2).matrix().charpoly('x')     # x^2 + x - 1
f.coefficient(13).matrix().charpoly('x')    # x^2 - 6*x + 9
(P2)
PARI/GP
mf = mfinit([23, 2], 0);                    \\ new cuspidal space
charpoly(mfheckemat(mf, 13))                \\ x^2 - 6*x + 9
Links
Similar tables
Hecke polynomials of level one cusp forms —   stores characteristic polynomials of $T_p$ on level-one cusp-form spaces, while this table stores characteristic polynomials of $a_p$ on individual coefficient fields in weight $2$
$q$-expansion of the modular discriminant $\Delta$ —   its Ramanujan tau coefficients are the Hecke eigenvalues of the unique level-one weight $12$ newform
Spectral parameter of Maass forms of level 1 —   stores spectral data for non-holomorphic automorphic eigenforms for $\mathrm{SL}_2(\mathbb{Z})$
Data properties
Entries are of type: integral polynomial
How well the digits are known: exact
Table is complete: no (it holds every weight $2$ newform orbit of trivial character and level $N\leq100$ whose coefficient field has degree at least $2$, for the primes $p\leq59$ at which $a_p$ generates that field)
How they were obtained:

The generator enumerates Sage's Newforms(N, 2) [7] for $N\leq100$, uses the LMFDB label order [5] [6], and keeps exactly the $50$ orbits whose coefficient field has degree at least $2$.

more

For each retained orbit and each prime $p\leq59$, it takes the exact Sage coefficient $a_p$, builds the multiplication matrix of $a_p$ on $K_f$, and computes $\det(xI-m_{a_p})$ by a permutation expansion over $\mathbb{Q}$, keeping the row when that polynomial is irreducible, which is to say when $a_p$ generates $K_f$. Before the draft was created, the labels and degrees were compared with the LMFDB API data, including the LMFDB page for 23.2.a.a [4]. For every level $N\leq100$ and every prime $p\leq59$, the product of the polynomials over all newform orbits, including dimension-one orbits omitted from the table, was required to equal PARI/GP's charpoly(mfheckemat(mfinit([N,2],0),p)) [8].



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