# Properties

 Base field $$\Q(\sqrt{5})$$ Weight [2, 2] Level norm 500 Level $[500, 50, -20w + 10]$ Label 2.2.5.1-500.1-a Dimension 2 CM no Base change no

# Related objects

## Base field $$\Q(\sqrt{5})$$

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

## Form

 Weight [2, 2] Level $[500, 50, -20w + 10]$ Label 2.2.5.1-500.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - 5x - 25$$
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -2w + 1]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}0$
11 $[11, 11, -3w + 2]$ $\phantom{-}2$
11 $[11, 11, -3w + 1]$ $\phantom{-}2$
19 $[19, 19, -4w + 3]$ $\phantom{-}e$
19 $[19, 19, -4w + 1]$ $-e + 5$
29 $[29, 29, w + 5]$ $\phantom{-}e$
29 $[29, 29, -w + 6]$ $-e + 5$
31 $[31, 31, -5w + 2]$ $-e + 2$
31 $[31, 31, -5w + 3]$ $\phantom{-}e - 3$
41 $[41, 41, -6w + 5]$ $-e + 2$
41 $[41, 41, w - 7]$ $\phantom{-}e - 3$
49 $[49, 7, -7]$ $-10$
59 $[59, 59, 2w - 9]$ $-e - 5$
59 $[59, 59, 7w - 5]$ $\phantom{-}e - 10$
61 $[61, 61, 3w - 10]$ $-2e + 2$
61 $[61, 61, -3w - 7]$ $\phantom{-}2e - 8$
71 $[71, 71, -8w + 7]$ $\phantom{-}e - 8$
71 $[71, 71, w - 9]$ $-e - 3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $1$
5 $[5, 5, -2w + 1]$ $1$