# Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 5, 2w^{2} - 2w - 13]$ Label 4.4.17725.1-25.1-a Dimension 2 CM no Base change no

# Related objects

• L-function not available

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## Base field 4.4.17725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 12x^{2} + 13x + 41$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[25, 5, 2w^{2} - 2w - 13]$ Label 4.4.17725.1-25.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 49

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 4x$$ $$\mathstrut -\mathstrut 8$$
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $-e - 4$
16 $[16, 2, 2]$ $\phantom{-}0$
19 $[19, 19, w + 1]$ $-\frac{3}{2}e - 4$
19 $[19, 19, -w^{2} + 6]$ $-\frac{3}{2}e$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}\frac{3}{2}e + 6$
19 $[19, 19, -w + 2]$ $\phantom{-}\frac{3}{2}e + 2$
25 $[25, 5, 2w^{2} - 2w - 13]$ $\phantom{-}1$
29 $[29, 29, -w^{2} + 9]$ $-\frac{1}{2}e + 4$
29 $[29, 29, -w^{2} + 2w + 6]$ $-e - 6$
29 $[29, 29, w^{2} - 7]$ $\phantom{-}e - 2$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}\frac{1}{2}e + 6$
31 $[31, 31, -2w^{2} + w + 12]$ $\phantom{-}e + 6$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-e + 2$
41 $[41, 41, -w]$ $\phantom{-}2e + 7$
41 $[41, 41, -w + 1]$ $-2e - 1$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $\phantom{-}\frac{1}{2}e - 6$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-\frac{1}{2}e - 8$
61 $[61, 61, 2w^{2} - 3w - 14]$ $-e - 9$
61 $[61, 61, 2w^{2} - w - 15]$ $\phantom{-}e - 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
25 $[25, 5, 2w^{2} - 2w - 13]$ $-1$