# Properties

 Label 2.2.8.1-71.1-a Base field $$\Q(\sqrt{2})$$ Weight $[2, 2]$ Level norm $71$ Level $[71, 71, -6w - 1]$ 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: $[71, 71, -6w - 1]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $2$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 3$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
7 $[7, 7, -2w + 1]$ $\phantom{-}e + 2$
7 $[7, 7, -2w - 1]$ $-2e - 1$
9 $[9, 3, 3]$ $-2$
17 $[17, 17, 3w + 1]$ $-2e$
17 $[17, 17, 3w - 1]$ $-e$
23 $[23, 23, w + 5]$ $\phantom{-}2e + 6$
23 $[23, 23, -w + 5]$ $\phantom{-}6$
25 $[25, 5, 5]$ $-7$
31 $[31, 31, 4w + 1]$ $\phantom{-}2e + 2$
31 $[31, 31, -4w + 1]$ $\phantom{-}2$
41 $[41, 41, 2w - 7]$ $-2e$
41 $[41, 41, -2w - 7]$ $\phantom{-}4e - 3$
47 $[47, 47, -w - 7]$ $-6e$
47 $[47, 47, w - 7]$ $\phantom{-}2e - 3$
71 $[71, 71, -6w - 1]$ $-1$
71 $[71, 71, 6w - 1]$ $\phantom{-}e - 6$
73 $[73, 73, -7w - 5]$ $\phantom{-}e - 4$
73 $[73, 73, 7w - 5]$ $\phantom{-}3e - 4$
79 $[79, 79, -w - 9]$ $\phantom{-}3e - 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$71$ $[71, 71, -6w - 1]$ $1$