# Properties

 Base field $\Q(\sqrt{5})$ Weight [2, 2] Level norm 31 Level $[31, 31, -5w + 2]$ Label 2.2.5.1-31.1-a Dimension 1 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 $[31, 31, -5w + 2]$ Label 2.2.5.1-31.1-a Dimension 1 Is CM no Is base change no Parent newspace dimension 1

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-3$
5 $[5, 5, -2w + 1]$ $-2$
9 $[9, 3, 3]$ $2$
11 $[11, 11, -3w + 2]$ $4$
11 $[11, 11, -3w + 1]$ $-4$
19 $[19, 19, -4w + 3]$ $-4$
19 $[19, 19, -4w + 1]$ $4$
29 $[29, 29, w + 5]$ $-2$
29 $[29, 29, -w + 6]$ $-2$
31 $[31, 31, -5w + 2]$ $-1$
31 $[31, 31, -5w + 3]$ $8$
41 $[41, 41, -6w + 5]$ $-6$
41 $[41, 41, w - 7]$ $-6$
49 $[49, 7, -7]$ $2$
59 $[59, 59, 2w - 9]$ $12$
59 $[59, 59, 7w - 5]$ $-4$
61 $[61, 61, 3w - 10]$ $6$
61 $[61, 61, -3w - 7]$ $-2$
71 $[71, 71, -8w + 7]$ $0$
71 $[71, 71, w - 9]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, -5w + 2]$ $1$