# Properties

 Label 2.2.8.1-576.1-a Base field $$\Q(\sqrt{2})$$ Weight $[2, 2]$ Level norm $576$ Level $[576, 24, 24]$ Dimension $2$ CM no Base change no

# Related objects

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

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

## Form

 Weight: $[2, 2]$ Level: $[576, 24, 24]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{2} - 4x - 4$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}0$
7 $[7, 7, -2w + 1]$ $-e + 4$
7 $[7, 7, -2w - 1]$ $\phantom{-}e$
9 $[9, 3, 3]$ $-1$
17 $[17, 17, 3w + 1]$ $-2e + 2$
17 $[17, 17, 3w - 1]$ $\phantom{-}2e - 6$
23 $[23, 23, w + 5]$ $\phantom{-}4$
23 $[23, 23, -w + 5]$ $\phantom{-}4$
25 $[25, 5, 5]$ $-2$
31 $[31, 31, 4w + 1]$ $\phantom{-}e + 4$
31 $[31, 31, -4w + 1]$ $-e + 8$
41 $[41, 41, 2w - 7]$ $-2e + 6$
41 $[41, 41, -2w - 7]$ $\phantom{-}2e - 2$
47 $[47, 47, -w - 7]$ $-2e$
47 $[47, 47, w - 7]$ $\phantom{-}2e - 8$
71 $[71, 71, -6w - 1]$ $-4$
71 $[71, 71, 6w - 1]$ $-4$
73 $[73, 73, -7w - 5]$ $\phantom{-}2$
73 $[73, 73, 7w - 5]$ $\phantom{-}2$
79 $[79, 79, -w - 9]$ $\phantom{-}5e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $1$
$9$ $[9, 3, 3]$ $1$