# Properties

 Base field $$\Q(\sqrt{109})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.109.1-9.1-c Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{109})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 27$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[9, 3, 3]$ Label 2.2.109.1-9.1-c Dimension 2 Is CM no Is base change no Parent newspace dimension 13

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 2x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $-1$
3 $[3, 3, w + 5]$ $\phantom{-}1$
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, -3w + 17]$ $\phantom{-}2e + 1$
5 $[5, 5, -3w - 14]$ $-1$
7 $[7, 7, w - 5]$ $\phantom{-}e + 1$
7 $[7, 7, w + 4]$ $-3e - 3$
29 $[29, 29, -w - 7]$ $-e - 6$
29 $[29, 29, -w + 8]$ $-3e - 4$
31 $[31, 31, -5w + 28]$ $-2e - 8$
31 $[31, 31, -5w - 23]$ $-2e$
43 $[43, 43, 6w + 29]$ $-e + 3$
43 $[43, 43, -6w + 35]$ $-5e - 1$
61 $[61, 61, 3w - 19]$ $\phantom{-}2e - 9$
61 $[61, 61, -3w - 16]$ $\phantom{-}2e + 7$
71 $[71, 71, -7w - 34]$ $\phantom{-}7e + 7$
71 $[71, 71, 7w - 41]$ $\phantom{-}3e + 7$
73 $[73, 73, 2w - 7]$ $-8e - 11$
73 $[73, 73, -2w - 5]$ $\phantom{-}4e + 9$
83 $[83, 83, -w - 10]$ $-e - 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $1$
3 $[3, 3, w + 5]$ $-1$