Properties

Label 6.6.1541581.1-37.1-c
Base field 6.6.1541581.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $37$
Level $[37, 37, -w^{2} + 2w + 2]$
Dimension $25$
CM no
Base change no

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Base field 6.6.1541581.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[37, 37, -w^{2} + 2w + 2]$
Dimension: $25$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

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

\(x^{25} - 6x^{24} - 67x^{23} + 451x^{22} + 1752x^{21} - 14167x^{20} - 21349x^{19} + 241859x^{18} + 87730x^{17} - 2447889x^{16} + 693065x^{15} + 15064413x^{14} - 10241501x^{13} - 55671511x^{12} + 52588433x^{11} + 117028782x^{10} - 135924132x^{9} - 121318157x^{8} + 177064286x^{7} + 35792670x^{6} - 99002915x^{5} + 16333415x^{4} + 15597536x^{3} - 6507090x^{2} + 823332x - 28440\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ $\phantom{-}e$
11 $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ $...$
11 $[11, 11, w^{2} - w - 2]$ $...$
17 $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ $...$
27 $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ $...$
27 $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $...$
37 $[37, 37, -w^{2} + 2w + 2]$ $-1$
47 $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ $...$
53 $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ $...$
59 $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ $...$
64 $[64, 2, -2]$ $...$
67 $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ $...$
67 $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ $...$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $...$
71 $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $...$
73 $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ $...$
83 $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ $...$
83 $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ $...$
89 $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ $...$
97 $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, -w^{2} + 2w + 2]$ $1$