Properties

Label 6.6.1241125.1-41.1-d
Base field 6.6.1241125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$
Dimension $13$
CM no
Base change no

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Base field 6.6.1241125.1

Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$
Dimension: $13$
CM: no
Base change: no
Newspace dimension: $31$

Hecke eigenvalues ($q$-expansion)

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

\(x^{13} + 9x^{12} + 8x^{11} - 127x^{10} - 303x^{9} + 428x^{8} + 1644x^{7} - 149x^{6} - 3203x^{5} - 1013x^{4} + 2239x^{3} + 940x^{2} - 484x - 222\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $\phantom{-}e$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $...$
11 $[11, 11, w - 1]$ $...$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $...$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $...$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}1$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $...$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $...$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $...$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $...$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $...$
64 $[64, 2, 2]$ $...$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $...$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $...$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $...$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $...$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $...$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $...$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $...$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-1$