# Properties

 Base field $$\Q(\sqrt{5})$$ Weight [2, 2] Level norm 109 Level $[109, 109, -11w - 1]$ Label 2.2.5.1-109.1-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 $[109, 109, -11w - 1]$ Label 2.2.5.1-109.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

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

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
109 $[109, 109, -11w - 1]$ $1$