# Properties

 Label 2.2.17.1-512.2-f Base field $$\Q(\sqrt{17})$$ Weight $[2, 2]$ Level norm $512$ Level $[512,32,16w + 16]$ Dimension $1$ CM no Base change no

# Related objects

## Base field $$\Q(\sqrt{17})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 4$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[512,32,16w + 16]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}0$
2 $[2, 2, -w - 1]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}2$
13 $[13, 13, -2w + 3]$ $\phantom{-}2$
13 $[13, 13, 2w + 1]$ $-6$
17 $[17, 17, -2w + 1]$ $-2$
19 $[19, 19, -2w + 7]$ $-8$
19 $[19, 19, 2w + 5]$ $-4$
25 $[25, 5, -5]$ $\phantom{-}6$
43 $[43, 43, 4w - 7]$ $-4$
43 $[43, 43, 4w + 3]$ $-8$
47 $[47, 47, -2w + 9]$ $-8$
47 $[47, 47, 2w + 7]$ $\phantom{-}8$
49 $[49, 7, -7]$ $-2$
53 $[53, 53, 4w - 13]$ $-2$
53 $[53, 53, 6w - 13]$ $-10$
59 $[59, 59, -4w - 1]$ $\phantom{-}12$
59 $[59, 59, 4w - 5]$ $-8$
67 $[67, 67, 4w - 3]$ $\phantom{-}0$
67 $[67, 67, 4w - 1]$ $\phantom{-}4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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