# 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-b Dimension 4 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-b Dimension 4 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:
$$x^{4}$$ $$\mathstrut -\mathstrut 2x^{3}$$ $$\mathstrut -\mathstrut 6x^{2}$$ $$\mathstrut +\mathstrut 12x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{7}{2}e - \frac{5}{2}$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - \frac{19}{2}e + \frac{9}{2}$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{3} - e^{2} + 5e + 7$
19 $[19, 19, w^{2} - w + 1]$ $-e^{2} + 5$
23 $[23, 23, 2w - 3]$ $\phantom{-}e^{2} - 9$
27 $[27, 3, 3]$ $-e^{3} - e^{2} + 7e + 3$
29 $[29, 29, 2w + 1]$ $\phantom{-}2e^{3} - e^{2} - 12e + 5$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}1$
37 $[37, 37, 2w^{2} - 2w - 5]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{3}{2}$
41 $[41, 41, 2w^{2} - 9]$ $-e^{3} + 5e - 2$
43 $[43, 43, w^{2} + w - 5]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{3}{2}e^{2} - \frac{19}{2}e + \frac{11}{2}$
43 $[43, 43, -3w^{2} + w + 15]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{11}{2}e - \frac{17}{2}$
43 $[43, 43, -2w^{2} + 2w + 11]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 8$
53 $[53, 53, w^{2} - w - 7]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{11}{2}e + \frac{7}{2}$
61 $[61, 61, 4w^{2} - 2w - 15]$ $\phantom{-}e^{3} - 9e + 6$
67 $[67, 67, -5w^{2} + 3w + 23]$ $-e^{3} + 2e^{2} + 3e - 12$
73 $[73, 73, 2w^{2} - 3]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e + \frac{13}{2}$
73 $[73, 73, -3w^{2} - w + 7]$ $\phantom{-}e^{3} + e^{2} - 5e + 5$
73 $[73, 73, -6w^{2} + 4w + 25]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{7}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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