Properties

Base field 6.6.1241125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 41
Level $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$
Label 6.6.1241125.1-41.1-d
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 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$
Label 6.6.1241125.1-41.1-d
Dimension 13
Is CM no
Is base change no
Parent newspace dimension 31

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{13} \) \(\mathstrut +\mathstrut 9x^{12} \) \(\mathstrut +\mathstrut 8x^{11} \) \(\mathstrut -\mathstrut 127x^{10} \) \(\mathstrut -\mathstrut 303x^{9} \) \(\mathstrut +\mathstrut 428x^{8} \) \(\mathstrut +\mathstrut 1644x^{7} \) \(\mathstrut -\mathstrut 149x^{6} \) \(\mathstrut -\mathstrut 3203x^{5} \) \(\mathstrut -\mathstrut 1013x^{4} \) \(\mathstrut +\mathstrut 2239x^{3} \) \(\mathstrut +\mathstrut 940x^{2} \) \(\mathstrut -\mathstrut 484x \) \(\mathstrut -\mathstrut 222\)

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