# Properties

 Label 2.2.13.1-576.2-m Base field $$\Q(\sqrt{13})$$ Weight $[2, 2]$ Level norm $576$ Level $[576, 72, 8w + 24]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{13})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 3$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[576, 72, 8w + 24]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $19$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - x - 4$$
Norm Prime Eigenvalue
3 $[3, 3, -w]$ $\phantom{-}0$
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}0$
13 $[13, 13, -2w + 1]$ $\phantom{-}2e + 2$
17 $[17, 17, w + 4]$ $\phantom{-}e - 2$
17 $[17, 17, -w + 5]$ $-e + 2$
23 $[23, 23, 3w + 1]$ $\phantom{-}2e$
23 $[23, 23, -3w + 4]$ $-2e$
25 $[25, 5, 5]$ $\phantom{-}e - 6$
29 $[29, 29, 3w - 2]$ $\phantom{-}2e - 2$
29 $[29, 29, -3w + 1]$ $-2e + 2$
43 $[43, 43, -4w - 1]$ $-e + 8$
43 $[43, 43, 4w - 5]$ $-e + 8$
49 $[49, 7, -7]$ $-5e + 6$
53 $[53, 53, -w - 7]$ $-4e + 6$
53 $[53, 53, w - 8]$ $\phantom{-}4e - 6$
61 $[61, 61, -3w - 8]$ $-2e - 6$
61 $[61, 61, 3w - 11]$ $-2e - 6$
79 $[79, 79, 5w - 4]$ $-2e + 8$
79 $[79, 79, 5w - 1]$ $-2e + 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w]$ $-1$
$4$ $[4, 2, 2]$ $-1$