Properties

Label 6.6.1134389.1-37.2-a
Base field 6.6.1134389.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $37$
Level $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$
Dimension $13$
CM no
Base change no

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Base field 6.6.1134389.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$
Dimension: $13$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{13} - 10x^{12} - 12x^{11} + 384x^{10} - 582x^{9} - 4692x^{8} + 11569x^{7} + 22188x^{6} - 71620x^{5} - 32256x^{4} + 157213x^{3} - 6566x^{2} - 82704x + 16032\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{2} - w - 2]$ $\phantom{-}e$
13 $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $...$
17 $[17, 17, -w^{3} + w^{2} + 3w]$ $...$
19 $[19, 19, w^{3} - w^{2} - 3w + 1]$ $...$
19 $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $...$
23 $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ $...$
31 $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ $...$
37 $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $...$
37 $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ $-1$
47 $[47, 47, -w^{3} + 2w^{2} + w - 3]$ $...$
64 $[64, 2, -2]$ $...$
67 $[67, 67, 2w - 1]$ $...$
79 $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ $...$
79 $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ $...$
97 $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ $...$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ $...$
101 $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ $...$
101 $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ $...$
103 $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ $...$
107 $[107, 107, w^{2} - 2w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37,37,-w^{5}+2w^{4}+4w^{3}-6w^{2}-4w+1]$ $1$