# Properties

 Base field $$\Q(\sqrt{2})$$ Weight [2, 2] Level norm 89 Level $[89, 89, -4w - 11]$ Label 2.2.8.1-89.1-c 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 $[89, 89, -4w - 11]$ Label 2.2.8.1-89.1-c Dimension 2 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 3x$$ $$\mathstrut -\mathstrut 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}2$
7 $[7, 7, -2w + 1]$ $\phantom{-}e$
7 $[7, 7, -2w - 1]$ $-2e - 4$
9 $[9, 3, 3]$ $\phantom{-}2e + 2$
17 $[17, 17, 3w + 1]$ $-3e - 4$
17 $[17, 17, 3w - 1]$ $\phantom{-}e$
23 $[23, 23, w + 5]$ $-e - 4$
23 $[23, 23, -w + 5]$ $\phantom{-}2e + 4$
25 $[25, 5, 5]$ $-e + 4$
31 $[31, 31, 4w + 1]$ $-2e$
31 $[31, 31, -4w + 1]$ $\phantom{-}2e + 2$
41 $[41, 41, 2w - 7]$ $\phantom{-}e + 4$
41 $[41, 41, -2w - 7]$ $\phantom{-}10$
47 $[47, 47, -w - 7]$ $\phantom{-}2e + 2$
47 $[47, 47, w - 7]$ $-e - 4$
71 $[71, 71, -6w - 1]$ $-3e - 4$
71 $[71, 71, 6w - 1]$ $-2e - 2$
73 $[73, 73, -7w - 5]$ $-2e - 14$
73 $[73, 73, 7w - 5]$ $-4e - 10$
79 $[79, 79, -w - 9]$ $\phantom{-}5e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
89 $[89, 89, -4w - 11]$ $1$