# Properties

 Base field $$\Q(\sqrt{109})$$ Weight [2, 2] Level norm 3 Level $[3, 3, -w + 6]$ Label 2.2.109.1-3.1-a Dimension 2 CM no Base change no

# Related objects

## 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 $[3, 3, -w + 6]$ Label 2.2.109.1-3.1-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:
$$x^{2}$$ $$\mathstrut -\mathstrut 2x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $-1$
3 $[3, 3, w + 5]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}e - 2$
5 $[5, 5, -3w + 17]$ $-2$
5 $[5, 5, -3w - 14]$ $\phantom{-}e + 2$
7 $[7, 7, w - 5]$ $-2e + 4$
7 $[7, 7, w + 4]$ $\phantom{-}2e - 3$
29 $[29, 29, -w - 7]$ $-1$
29 $[29, 29, -w + 8]$ $-4e + 6$
31 $[31, 31, -5w + 28]$ $-4e + 4$
31 $[31, 31, -5w - 23]$ $-3e + 8$
43 $[43, 43, 6w + 29]$ $-6$
43 $[43, 43, -6w + 35]$ $\phantom{-}2e + 2$
61 $[61, 61, 3w - 19]$ $\phantom{-}9$
61 $[61, 61, -3w - 16]$ $\phantom{-}4e + 2$
71 $[71, 71, -7w - 34]$ $\phantom{-}6e - 3$
71 $[71, 71, 7w - 41]$ $-8e + 10$
73 $[73, 73, 2w - 7]$ $-4e - 4$
73 $[73, 73, -2w - 5]$ $-2e + 4$
83 $[83, 83, -w - 10]$ $-4e + 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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