# Properties

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

# Related objects

This Hilbert newform and its Galois conjugate have the smallest level norm.

## 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: $[31, 31, -5w + 2]$ Dimension: $1$ CM: no Base change: no 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 $[9, 3, 3]$ $\phantom{-}2$
11 $[11, 11, -3w + 2]$ $\phantom{-}4$
11 $[11, 11, -3w + 1]$ $-4$
19 $[19, 19, -4w + 3]$ $-4$
19 $[19, 19, -4w + 1]$ $\phantom{-}4$
29 $[29, 29, w + 5]$ $-2$
29 $[29, 29, -w + 6]$ $-2$
31 $[31, 31, -5w + 2]$ $-1$
31 $[31, 31, -5w + 3]$ $\phantom{-}8$
41 $[41, 41, -6w + 5]$ $-6$
41 $[41, 41, w - 7]$ $-6$
49 $[49, 7, -7]$ $\phantom{-}2$
59 $[59, 59, 2w - 9]$ $\phantom{-}12$
59 $[59, 59, 7w - 5]$ $-4$
61 $[61, 61, 3w - 10]$ $\phantom{-}6$
61 $[61, 61, -3w - 7]$ $-2$
71 $[71, 71, -8w + 7]$ $\phantom{-}0$
71 $[71, 71, w - 9]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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