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-b
Dimension 5
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-b
Dimension 5
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:
\(x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut -\mathstrut 10x^{3} \) \(\mathstrut +\mathstrut 18x^{2} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut -\mathstrut 2\)

  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 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $-e^{4} + 10e^{2} - 7e - 4$
11 $[11, 11, w - 1]$ $-2e^{4} + 19e^{2} - 18e - 2$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}e^{4} - 10e^{2} + 10e + 4$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 7e + 8$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-1$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $-2e^{4} + 2e^{3} + 22e^{2} - 32e$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $-e^{4} + 10e^{2} - 10e - 2$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $-3e^{4} + 29e^{2} - 24e - 6$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $-2e^{2} - 2e + 12$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $\phantom{-}e^{4} - 10e^{2} + 8e - 4$
64 $[64, 2, 2]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 8e + 3$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $-4e^{3} - 4e^{2} + 30e - 8$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $\phantom{-}e^{2} + 2e + 4$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $-e^{4} - 2e^{3} + 9e^{2} + 8e - 4$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $-5e^{4} + 47e^{2} - 46e - 2$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $-2e^{4} + 18e^{2} - 19e + 4$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $\phantom{-}4e^{4} + e^{3} - 38e^{2} + 26e + 12$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $-5e^{4} + 48e^{2} - 46e - 6$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $-3e^{4} + 30e^{2} - 26e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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