Properties

Base field 6.6.1397493.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 37
Level $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$
Label 6.6.1397493.1-37.1-a
Dimension 1
CM no
Base change no

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Base field 6.6.1397493.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$
Label 6.6.1397493.1-37.1-a
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 38

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $-3$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}3$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $-3$
19 $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ $\phantom{-}2$
19 $[19, 19, w^{2} - w - 1]$ $\phantom{-}5$
37 $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ $\phantom{-}1$
37 $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ $-10$
53 $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ $\phantom{-}12$
53 $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ $-12$
64 $[64, 2, -2]$ $-1$
71 $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ $\phantom{-}9$
71 $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ $-12$
71 $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ $-12$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ $-7$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ $\phantom{-}2$
89 $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ $-6$
89 $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ $-15$
89 $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ $\phantom{-}12$
89 $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ $\phantom{-}12$
107 $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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