# Properties

 Base field 3.3.316.1 Weight [2, 2, 2] Level norm 31 Level $[31, 31, 2w^{2} - 2w - 9]$ Label 3.3.316.1-31.1-a Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.316.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 4x + 2$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[31, 31, 2w^{2} - 2w - 9]$ Label 3.3.316.1-31.1-a Dimension 3 Is CM no Is base change no Parent newspace dimension 11

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut 2x^{2}$$ $$\mathstrut -\mathstrut 2x$$ $$\mathstrut +\mathstrut 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $-e + 1$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}e^{2} - e - 4$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}2e^{2} - e - 2$
19 $[19, 19, w^{2} - w + 1]$ $-2e^{2} + 2e + 2$
23 $[23, 23, 2w - 3]$ $\phantom{-}e^{2} - 3e + 4$
27 $[27, 3, 3]$ $-e^{2} - e$
29 $[29, 29, 2w + 1]$ $-2e^{2} + e + 10$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}1$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-2e^{2} + 3e + 2$
41 $[41, 41, 2w^{2} - 9]$ $\phantom{-}3e^{2} - 4e + 2$
43 $[43, 43, w^{2} + w - 5]$ $\phantom{-}4e^{2} - 6e - 4$
43 $[43, 43, -3w^{2} + w + 15]$ $-e^{2} + 2e + 2$
43 $[43, 43, -2w^{2} + 2w + 11]$ $\phantom{-}4$
53 $[53, 53, w^{2} - w - 7]$ $\phantom{-}e^{2}$
61 $[61, 61, 4w^{2} - 2w - 15]$ $-e^{2} - 4e + 8$
67 $[67, 67, -5w^{2} + 3w + 23]$ $\phantom{-}2e^{2} + 2e - 6$
73 $[73, 73, 2w^{2} - 3]$ $\phantom{-}e^{2} - 8e + 4$
73 $[73, 73, -3w^{2} - w + 7]$ $-3e^{2} + 6e - 2$
73 $[73, 73, -6w^{2} + 4w + 25]$ $-2e^{2} + 7e + 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, 2w^{2} - 2w - 9]$ $-1$