Properties

 Label 2.2.8.1-49.2-a Base field $$\Q(\sqrt{2})$$ Weight $[2, 2]$ Level norm $49$ Level $[49, 49, 5w + 1]$ 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: $[49, 49, 5w + 1]$ 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:

 $$x^{2} - 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
7 $[7, 7, -2w + 1]$ $\phantom{-}0$
7 $[7, 7, -2w - 1]$ $-2e$
9 $[9, 3, 3]$ $\phantom{-}e$
17 $[17, 17, 3w + 1]$ $\phantom{-}4$
17 $[17, 17, 3w - 1]$ $-e$
23 $[23, 23, w + 5]$ $-4$
23 $[23, 23, -w + 5]$ $-4$
25 $[25, 5, 5]$ $-3e$
31 $[31, 31, 4w + 1]$ $\phantom{-}4$
31 $[31, 31, -4w + 1]$ $\phantom{-}6e$
41 $[41, 41, 2w - 7]$ $\phantom{-}7e$
41 $[41, 41, -2w - 7]$ $\phantom{-}0$
47 $[47, 47, -w - 7]$ $-8$
47 $[47, 47, w - 7]$ $\phantom{-}2e$
71 $[71, 71, -6w - 1]$ $\phantom{-}10e$
71 $[71, 71, 6w - 1]$ $-4e$
73 $[73, 73, -7w - 5]$ $\phantom{-}4$
73 $[73, 73, 7w - 5]$ $-e$
79 $[79, 79, -w - 9]$ $\phantom{-}8e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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