# Properties

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

# 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-d Dimension 3 Is CM no Is base change yes Parent newspace dimension 13

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut 4x^{2}$$ $$\mathstrut -\mathstrut 6x$$ $$\mathstrut +\mathstrut 25$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $-1$
3 $[3, 3, w + 5]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, -3w + 17]$ $-2$
5 $[5, 5, -3w - 14]$ $-2$
7 $[7, 7, w - 5]$ $-e^{2} + e + 8$
7 $[7, 7, w + 4]$ $-e^{2} + e + 8$
29 $[29, 29, -w - 7]$ $-2e^{2} + 2e + 14$
29 $[29, 29, -w + 8]$ $-2e^{2} + 2e + 14$
31 $[31, 31, -5w + 28]$ $\phantom{-}e^{2} + e - 10$
31 $[31, 31, -5w - 23]$ $\phantom{-}e^{2} + e - 10$
43 $[43, 43, 6w + 29]$ $-e^{2} + 3e + 2$
43 $[43, 43, -6w + 35]$ $-e^{2} + 3e + 2$
61 $[61, 61, 3w - 19]$ $-e^{2} - e + 16$
61 $[61, 61, -3w - 16]$ $-e^{2} - e + 16$
71 $[71, 71, -7w - 34]$ $-2e^{2} + 6e + 12$
71 $[71, 71, 7w - 41]$ $-2e^{2} + 6e + 12$
73 $[73, 73, 2w - 7]$ $\phantom{-}3e^{2} - 3e - 22$
73 $[73, 73, -2w - 5]$ $\phantom{-}3e^{2} - 3e - 22$
83 $[83, 83, -w - 10]$ $\phantom{-}2e^{2} - 2e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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