# Properties

 Base field 4.4.8069.1 Weight [2, 2, 2, 2] Level norm 17 Level $[17, 17, -w^{3} + 5w - 2]$ Label 4.4.8069.1-17.2-c Dimension 1 CM no Base change no

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## Base field 4.4.8069.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 5x^{2} + 5x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[17, 17, -w^{3} + 5w - 2]$ Label 4.4.8069.1-17.2-c Dimension 1 Is CM no Is base change no Parent newspace dimension 8

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}0$
7 $[7, 7, w + 1]$ $-4$
7 $[7, 7, -w^{3} + 4w - 1]$ $\phantom{-}2$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}2$
16 $[16, 2, 2]$ $\phantom{-}5$
17 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $-6$
17 $[17, 17, -w^{3} + 5w - 2]$ $-1$
19 $[19, 19, -w^{2} - w + 4]$ $-4$
19 $[19, 19, -w^{2} - w + 1]$ $\phantom{-}2$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $\phantom{-}0$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $-6$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}8$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}8$
47 $[47, 47, -w^{3} - w^{2} + 5w]$ $\phantom{-}12$
49 $[49, 7, w^{2} + 2w - 2]$ $\phantom{-}14$
59 $[59, 59, 2w^{3} - 8w + 3]$ $-6$
67 $[67, 67, w^{2} - w - 4]$ $\phantom{-}14$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}14$
81 $[81, 3, -3]$ $-2$
97 $[97, 97, w^{3} + w^{2} - 5w + 1]$ $-10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{3} + 5w - 2]$ $1$