# Properties

 Base field 4.4.6125.1 Weight [2, 2, 2, 2] Level norm 59 Level $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ Label 4.4.6125.1-59.1-d Dimension 1 CM no Base change no

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## Base field 4.4.6125.1

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

## Form

 Weight [2, 2, 2, 2] Level $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ Label 4.4.6125.1-59.1-d Dimension 1 Is CM no Is base change no Parent newspace dimension 20

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $-2$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $-1$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $-1$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $\phantom{-}2$
11 $[11, 11, w - 1]$ $-4$
16 $[16, 2, 2]$ $-5$
19 $[19, 19, -w^{2} + 4]$ $\phantom{-}5$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $-1$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $-1$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $-4$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $\phantom{-}4$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $-1$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $\phantom{-}0$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $\phantom{-}15$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $-3$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $\phantom{-}12$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $-3$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $\phantom{-}0$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $-9$
81 $[81, 3, -3]$ $-13$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $1$