# Properties

 Base field $$\Q(\sqrt{2}, \sqrt{5})$$ Weight [2, 2, 2, 2] Level norm 400 Level $[400, 10, 2w^{2} - 6]$ Label 4.4.1600.1-400.1-a Dimension 1 CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{2}, \sqrt{5})$$

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} + 4$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[400, 10, 2w^{2} - 6]$ Label 4.4.1600.1-400.1-a Dimension 1 Is CM no Is base change yes Parent newspace dimension 15

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 2w]$ $\phantom{-}0$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 3]$ $-2$
9 $[9, 3, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 3]$ $-2$
25 $[25, 5, w^{2} - 3]$ $\phantom{-}1$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w]$ $-4$
31 $[31, 31, -\frac{1}{2}w^{2} - w + 3]$ $-4$
31 $[31, 31, -\frac{1}{2}w^{2} + w + 3]$ $-4$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w]$ $-4$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - w + 3]$ $\phantom{-}6$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}6$
41 $[41, 41, -\frac{3}{2}w^{2} - w + 5]$ $\phantom{-}6$
41 $[41, 41, -\frac{1}{2}w^{3} - w^{2} + w + 3]$ $\phantom{-}6$
49 $[49, 7, -\frac{1}{2}w^{3} + 2w - 3]$ $-10$
49 $[49, 7, \frac{1}{2}w^{3} - 2w - 3]$ $-10$
71 $[71, 71, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 5]$ $-12$
71 $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 5]$ $-12$
71 $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 5]$ $-12$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 5]$ $-12$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 2w - 4]$ $\phantom{-}8$
79 $[79, 79, -w^{3} - \frac{1}{2}w^{2} + 6w]$ $\phantom{-}8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4,2,\frac{1}{2}w^{3}-2w]$ $1$
25 $[25,5,w^{2}-3]$ $-1$