# Properties

 Label 2.2.8.1-2304.1-f Base field $$\Q(\sqrt{2})$$ Weight $[2, 2]$ Level norm $2304$ Level $[2304, 48, 48]$ Dimension $1$ CM no Base change yes

# 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: $[2304, 48, 48]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $32$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}0$
7 $[7, 7, -2w + 1]$ $-2$
7 $[7, 7, -2w - 1]$ $-2$
9 $[9, 3, 3]$ $\phantom{-}1$
17 $[17, 17, 3w + 1]$ $-2$
17 $[17, 17, 3w - 1]$ $-2$
23 $[23, 23, w + 5]$ $-4$
23 $[23, 23, -w + 5]$ $-4$
25 $[25, 5, 5]$ $\phantom{-}6$
31 $[31, 31, 4w + 1]$ $\phantom{-}6$
31 $[31, 31, -4w + 1]$ $\phantom{-}6$
41 $[41, 41, 2w - 7]$ $\phantom{-}6$
41 $[41, 41, -2w - 7]$ $\phantom{-}6$
47 $[47, 47, -w - 7]$ $-4$
47 $[47, 47, w - 7]$ $-4$
71 $[71, 71, -6w - 1]$ $-12$
71 $[71, 71, 6w - 1]$ $-12$
73 $[73, 73, -7w - 5]$ $-10$
73 $[73, 73, 7w - 5]$ $-10$
79 $[79, 79, -w - 9]$ $-10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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