# Properties

 Base field $$\Q(\sqrt{2})$$ Weight [2, 2] Level norm 49 Level $[49, 7, 7]$ Label 2.2.8.1-49.1-b Dimension 2 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 $[49, 7, 7]$ Label 2.2.8.1-49.1-b Dimension 2 Is CM no Is base change yes Parent newspace dimension 3

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} + x - 4$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
7 $[7, 7, -2w + 1]$ $-1$
7 $[7, 7, -2w - 1]$ $-1$
9 $[9, 3, 3]$ $-2e$
17 $[17, 17, 3w + 1]$ $\phantom{-}2$
17 $[17, 17, 3w - 1]$ $\phantom{-}2$
23 $[23, 23, w + 5]$ $\phantom{-}2e + 2$
23 $[23, 23, -w + 5]$ $\phantom{-}2e + 2$
25 $[25, 5, 5]$ $\phantom{-}2e + 4$
31 $[31, 31, 4w + 1]$ $-4e - 4$
31 $[31, 31, -4w + 1]$ $-4e - 4$
41 $[41, 41, 2w - 7]$ $\phantom{-}4e - 2$
41 $[41, 41, -2w - 7]$ $\phantom{-}4e - 2$
47 $[47, 47, -w - 7]$ $\phantom{-}0$
47 $[47, 47, w - 7]$ $\phantom{-}0$
71 $[71, 71, -6w - 1]$ $-8$
71 $[71, 71, 6w - 1]$ $-8$
73 $[73, 73, -7w - 5]$ $-6$
73 $[73, 73, 7w - 5]$ $-6$
79 $[79, 79, -w - 9]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, -2w + 1]$ $1$
7 $[7, 7, -2w - 1]$ $1$