Properties

 Base field 6.6.1241125.1 Weight [2, 2, 2, 2, 2, 2] Level norm 45 Level $[45, 15, 2w^{5} - 14w^{3} - 3w^{2} + 23w + 9]$ Label 6.6.1241125.1-45.1-i Dimension 2 CM no Base change no

Related objects

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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 $[45, 15, 2w^{5} - 14w^{3} - 3w^{2} + 23w + 9]$ Label 6.6.1241125.1-45.1-i Dimension 2 Is CM no Is base change no Parent newspace dimension 27

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - 8x + 10$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $-1$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $\phantom{-}1$
11 $[11, 11, w - 1]$ $\phantom{-}e$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $-1$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $-5$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-2e + 9$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $\phantom{-}0$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $-3e + 4$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $\phantom{-}3e - 19$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $-e + 1$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $-3e + 16$
64 $[64, 2, 2]$ $-e + 3$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}e - 10$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $-3e + 17$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $\phantom{-}2e - 16$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $-e - 9$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $-5e + 25$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $\phantom{-}3e - 14$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $\phantom{-}5e - 20$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $\phantom{-}e - 8$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $1$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $-1$