Properties

Label 6.6.703493.1-41.4-e
Base field 6.6.703493.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41,41,3w^{5} - w^{4} - 18w^{3} + 4w^{2} + 20w + 1]$
Dimension $1$
CM no
Base change no

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Base field 6.6.703493.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41,41,3w^{5} - w^{4} - 18w^{3} + 4w^{2} + 20w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $11$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
13 $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ $-4$
13 $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ $\phantom{-}2$
13 $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ $-4$
13 $[13, 13, -w^{2} + 3]$ $-4$
41 $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ $\phantom{-}0$
41 $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ $-6$
41 $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $\phantom{-}0$
41 $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ $\phantom{-}1$
43 $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ $-4$
43 $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ $-4$
49 $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ $-4$
64 $[64, 2, -2]$ $-1$
71 $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ $\phantom{-}0$
71 $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ $\phantom{-}6$
83 $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ $\phantom{-}6$
83 $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ $-12$
97 $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ $\phantom{-}2$
97 $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ $\phantom{-}2$
113 $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ $\phantom{-}12$
113 $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ $\phantom{-}18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41,41,3w^{5} - w^{4} - 18w^{3} + 4w^{2} + 20w + 1]$ $-1$