# Properties

 Base field $$\Q(\sqrt{2})$$ Weight [2, 2] Level norm 79 Level $[79,79,w - 9]$ Label 2.2.8.1-79.2-a Dimension 3 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 $[79,79,w - 9]$ Label 2.2.8.1-79.2-a Dimension 3 Is CM no Is base change no Parent newspace dimension 3

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut +\mathstrut x^{2}$$ $$\mathstrut -\mathstrut 5x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
7 $[7, 7, -2w + 1]$ $-\frac{1}{2}e^{2} + \frac{5}{2}$
7 $[7, 7, -2w - 1]$ $-e + 1$
9 $[9, 3, 3]$ $-\frac{1}{2}e^{2} - 2e + \frac{1}{2}$
17 $[17, 17, 3w + 1]$ $\phantom{-}\frac{1}{2}e^{2} + 2e - \frac{5}{2}$
17 $[17, 17, 3w - 1]$ $-2$
23 $[23, 23, w + 5]$ $\phantom{-}\frac{5}{2}e^{2} + 2e - \frac{9}{2}$
23 $[23, 23, -w + 5]$ $-2e^{2} - 2e + 8$
25 $[25, 5, 5]$ $-e^{2} + e + 2$
31 $[31, 31, 4w + 1]$ $\phantom{-}\frac{3}{2}e^{2} - \frac{3}{2}$
31 $[31, 31, -4w + 1]$ $\phantom{-}e^{2} + 2e - 3$
41 $[41, 41, 2w - 7]$ $\phantom{-}2e^{2} + 4e - 8$
41 $[41, 41, -2w - 7]$ $\phantom{-}e^{2} - 3e - 8$
47 $[47, 47, -w - 7]$ $\phantom{-}2e + 2$
47 $[47, 47, w - 7]$ $\phantom{-}2e + 2$
71 $[71, 71, -6w - 1]$ $\phantom{-}3e^{2} - 15$
71 $[71, 71, 6w - 1]$ $-\frac{5}{2}e^{2} - 4e + \frac{13}{2}$
73 $[73, 73, -7w - 5]$ $\phantom{-}\frac{5}{2}e^{2} + 4e - \frac{1}{2}$
73 $[73, 73, 7w - 5]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}$
79 $[79, 79, -w - 9]$ $-3e^{2} - 2e + 13$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
79 $[79,79,w - 9]$ $1$