# Properties

 Base field $$\Q(\sqrt{2}, \sqrt{3})$$ Weight [2, 2, 2, 2] Level norm 25 Level $[25, 5, w^{3} - 5w - 1]$ Label 4.4.2304.1-25.2-a Dimension 4 CM no Base change yes

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{2}, \sqrt{3})$$

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

## Form

 Weight [2, 2, 2, 2] Level $[25, 5, w^{3} - 5w - 1]$ Label 4.4.2304.1-25.2-a Dimension 4 Is CM no Is base change yes Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 7x^{2} + 8$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 4w + 1]$ $\phantom{-}e$
9 $[9, 3, -w^{2} + 2]$ $-e^{2} + 6$
23 $[23, 23, w^{3} - w^{2} - 4w + 1]$ $-e^{3} + 4e$
23 $[23, 23, w^{2} - w - 3]$ $-e^{3} + 4e$
23 $[23, 23, -w^{2} - w + 3]$ $\phantom{-}2e^{3} - 10e$
23 $[23, 23, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}2e^{3} - 10e$
25 $[25, 5, w^{3} - 5w + 1]$ $-3e^{2} + 14$
25 $[25, 5, w^{3} - 5w - 1]$ $-1$
47 $[47, 47, -3w^{3} + 2w^{2} + 12w - 8]$ $\phantom{-}e^{3} - 6e$
47 $[47, 47, -2w^{3} - w^{2} + 6w]$ $\phantom{-}e^{3} - 6e$
47 $[47, 47, 2w^{3} - w^{2} - 6w]$ $-2e^{3} + 8e$
47 $[47, 47, w^{2} + w - 5]$ $-2e^{3} + 8e$
49 $[49, 7, 2w^{3} - 6w - 1]$ $-2$
49 $[49, 7, -2w^{3} + 6w - 1]$ $-2$
71 $[71, 71, 2w^{3} - w^{2} - 7w + 1]$ $-2e^{3} + 16e$
71 $[71, 71, 3w^{3} - w^{2} - 11w + 2]$ $-2e^{3} + 16e$
71 $[71, 71, 4w^{3} - 2w^{2} - 14w + 5]$ $-3e^{3} + 12e$
71 $[71, 71, -3w^{3} + 2w^{2} + 10w - 4]$ $-3e^{3} + 12e$
73 $[73, 73, -w^{3} - 2w^{2} + 3w + 5]$ $\phantom{-}4e^{2} - 14$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-3e^{2} + 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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