Properties

Label 5.5.65657.1-53.1-a
Base field 5.5.65657.1
Weight [2,2,2,2,2][2, 2, 2, 2, 2]
Level norm 5353
Level [53,53,w4+w3+4w2w4][53, 53, -w^4 + w^3 + 4 w^2 - w - 4]
Dimension 44
CM no
Base change no

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Base field 5.5.65657.1

Generator ww, with minimal polynomial x5x45x3+2x2+5x+1x^5 - x^4 - 5 x^3 + 2 x^2 + 5 x + 1; narrow class number 11 and class number 11.

Form

Weight: [2,2,2,2,2][2, 2, 2, 2, 2]
Level: [53,53,w4+w3+4w2w4][53, 53, -w^4 + w^3 + 4 w^2 - w - 4]
Dimension: 44
CM: no
Base change: no
Newspace dimension: 2222

Hecke eigenvalues (qq-expansion)

The Hecke eigenvalue field is Q(e)\Q(e) where ee is a root of the defining polynomial:

x42x37x2+18x9x^4 - 2 x^3 - 7 x^2 + 18 x - 9

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 [3,3,w4+w3+4w22w2][3, 3, -w^4 + w^3 + 4 w^2 - 2 w - 2] e\phantom{-}e
5 [5,5,w2w2][5, 5, w^2 - w - 2] 13e323e2103e+4\phantom{-}\frac{1}{3} e^3 - \frac{2}{3} e^2 - \frac{10}{3} e + 4
19 [19,19,w42w34w2+5w+4][19, 19, w^4 - 2 w^3 - 4 w^2 + 5 w + 4] 2e3+e2+15e16-2 e^3 + e^2 + 15 e - 16
23 [23,23,w3+w2+3w1][23, 23, -w^3 + w^2 + 3 w - 1] 13e3+23e2+103e10-\frac{1}{3} e^3 + \frac{2}{3} e^2 + \frac{10}{3} e - 10
29 [29,29,2w43w38w2+7w+4][29, 29, 2 w^4 - 3 w^3 - 8 w^2 + 7 w + 4] 103e383e2853e+31\phantom{-}\frac{10}{3} e^3 - \frac{8}{3} e^2 - \frac{85}{3} e + 31
32 [32,2,2][32, 2, 2] 113e3+73e2+833e29-\frac{11}{3} e^3 + \frac{7}{3} e^2 + \frac{83}{3} e - 29
37 [37,37,w32w22w+2][37, 37, w^3 - 2 w^2 - 2 w + 2] 23e3+73e2+173e16-\frac{2}{3} e^3 + \frac{7}{3} e^2 + \frac{17}{3} e - 16
41 [41,41,2w4+3w3+9w28w6][41, 41, -2 w^4 + 3 w^3 + 9 w^2 - 8 w - 6] 53e3+13e2+353e9-\frac{5}{3} e^3 + \frac{1}{3} e^2 + \frac{35}{3} e - 9
43 [43,43,2w4+3w3+8w28w6][43, 43, -2 w^4 + 3 w^3 + 8 w^2 - 8 w - 6] 23e343e2203e+11\phantom{-}\frac{2}{3} e^3 - \frac{4}{3} e^2 - \frac{20}{3} e + 11
47 [47,47,w42w35w2+6w+5][47, 47, w^4 - 2 w^3 - 5 w^2 + 6 w + 5] 3e3+21e15-3 e^3 + 21 e - 15
53 [53,53,w4+w3+4w2w4][53, 53, -w^4 + w^3 + 4 w^2 - w - 4] 1-1
61 [61,61,w22w3][61, 61, w^2 - 2 w - 3] e3+e27e3\phantom{-}e^3 + e^2 - 7 e - 3
67 [67,67,w4w34w2+3w][67, 67, w^4 - w^3 - 4 w^2 + 3 w] 23e383e243e+15-\frac{2}{3} e^3 - \frac{8}{3} e^2 - \frac{4}{3} e + 15
67 [67,67,w4+w3+5w22w2][67, 67, -w^4 + w^3 + 5 w^2 - 2 w - 2] 163e383e21093e+35\phantom{-}\frac{16}{3} e^3 - \frac{8}{3} e^2 - \frac{109}{3} e + 35
71 [71,71,w4w34w2+5][71, 71, w^4 - w^3 - 4 w^2 + 5] 143e343e2923e+28\phantom{-}\frac{14}{3} e^3 - \frac{4}{3} e^2 - \frac{92}{3} e + 28
71 [71,71,w42w33w2+5w+3][71, 71, w^4 - 2 w^3 - 3 w^2 + 5 w + 3] 3e3+e223e+13\phantom{-}3 e^3 + e^2 - 23 e + 13
71 [71,71,2w42w38w2+5w+4][71, 71, 2 w^4 - 2 w^3 - 8 w^2 + 5 w + 4] 23e383e2+143e+6-\frac{2}{3} e^3 - \frac{8}{3} e^2 + \frac{14}{3} e + 6
73 [73,73,2w4+2w3+9w25w6][73, 73, -2 w^4 + 2 w^3 + 9 w^2 - 5 w - 6] 103e3+13e2673e+14\phantom{-}\frac{10}{3} e^3 + \frac{1}{3} e^2 - \frac{67}{3} e + 14
81 [81,3,2w4+3w3+10w29w10][81, 3, -2 w^4 + 3 w^3 + 10 w^2 - 9 w - 10] 163e383e21123e+30\phantom{-}\frac{16}{3} e^3 - \frac{8}{3} e^2 - \frac{112}{3} e + 30
97 [97,97,2w4+3w3+7w25w4][97, 97, -2 w^4 + 3 w^3 + 7 w^2 - 5 w - 4] 13e3113e2103e+16\phantom{-}\frac{1}{3} e^3 - \frac{11}{3} e^2 - \frac{10}{3} e + 16
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5353 [53,53,w4+w3+4w2w4][53, 53, -w^4 + w^3 + 4 w^2 - w - 4] 11