# Properties

 Label 2.2.8.1-82.2-b Base field $$\Q(\sqrt{2})$$ Weight $[2, 2]$ Level norm $82$ Level $[82,82,-7w + 4]$ Dimension $1$ 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: $[82,82,-7w + 4]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $2$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $-1$
7 $[7, 7, -2w + 1]$ $\phantom{-}2$
7 $[7, 7, -2w - 1]$ $-1$
9 $[9, 3, 3]$ $\phantom{-}1$
17 $[17, 17, 3w + 1]$ $-3$
17 $[17, 17, 3w - 1]$ $\phantom{-}6$
23 $[23, 23, w + 5]$ $\phantom{-}0$
23 $[23, 23, -w + 5]$ $-6$
25 $[25, 5, 5]$ $\phantom{-}2$
31 $[31, 31, 4w + 1]$ $-7$
31 $[31, 31, -4w + 1]$ $\phantom{-}5$
41 $[41, 41, 2w - 7]$ $-1$
41 $[41, 41, -2w - 7]$ $\phantom{-}3$
47 $[47, 47, -w - 7]$ $-12$
47 $[47, 47, w - 7]$ $\phantom{-}3$
71 $[71, 71, -6w - 1]$ $-6$
71 $[71, 71, 6w - 1]$ $-3$
73 $[73, 73, -7w - 5]$ $\phantom{-}8$
73 $[73, 73, 7w - 5]$ $\phantom{-}8$
79 $[79, 79, -w - 9]$ $-10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,w]$ $1$
$41$ $[41,41,2w - 7]$ $1$