# Properties

 Base field 3.3.1101.1 Weight [2, 2, 2] Level norm 12 Level $[12, 6, w^{2} + w - 9]$ Label 3.3.1101.1-12.1-e Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1101.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 9x + 12$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[12, 6, w^{2} + w - 9]$ Label 3.3.1101.1-12.1-e Dimension 5 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:
$$x^{5}$$ $$\mathstrut -\mathstrut x^{4}$$ $$\mathstrut -\mathstrut 8x^{3}$$ $$\mathstrut +\mathstrut 6x^{2}$$ $$\mathstrut +\mathstrut 13x$$ $$\mathstrut -\mathstrut 3$$
Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $-1$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{1}{2}e^{4} - 3e^{2} + \frac{5}{2}$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}1$
19 $[19, 19, w + 1]$ $-e^{2} + 5$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}e^{3} - 2e^{2} - 5e + 6$
31 $[31, 31, -2w^{2} + 19]$ $-\frac{3}{2}e^{4} + 9e^{2} - e - \frac{5}{2}$
31 $[31, 31, -w^{2} + 5]$ $-\frac{1}{2}e^{4} + e^{3} + 3e^{2} - 5e - \frac{5}{2}$
31 $[31, 31, -3w + 5]$ $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - 4e^{2} + 11e + \frac{13}{2}$
41 $[41, 41, w^{2} + 2w - 7]$ $-e^{3} + 3e$
43 $[43, 43, w^{2} - 11]$ $-\frac{1}{2}e^{4} - e^{3} + 2e^{2} + 4e + \frac{7}{2}$
47 $[47, 47, 3w - 7]$ $-\frac{1}{2}e^{4} + e^{3} - 4e + \frac{15}{2}$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}\frac{1}{2}e^{4} + 2e^{3} - 2e^{2} - 10e - \frac{9}{2}$
59 $[59, 59, 2w - 1]$ $\phantom{-}\frac{3}{2}e^{4} - e^{3} - 8e^{2} + 3e + \frac{9}{2}$
67 $[67, 67, 2w^{2} + w - 19]$ $-e^{4} - e^{3} + 8e^{2} + 7e - 13$
67 $[67, 67, 3w^{2} + 2w - 25]$ $-e^{4} + e^{3} + 8e^{2} - 9e - 7$
67 $[67, 67, w - 5]$ $\phantom{-}\frac{1}{2}e^{4} - 2e^{2} + 4e - \frac{5}{2}$
73 $[73, 73, -4w^{2} - 3w + 29]$ $-e^{4} - 2e^{3} + 7e^{2} + 10e - 4$
73 $[73, 73, 2w^{2} - w - 11]$ $\phantom{-}\frac{3}{2}e^{4} - 3e^{3} - 11e^{2} + 14e + \frac{25}{2}$
73 $[73, 73, w^{2} + 2w - 11]$ $\phantom{-}2e^{3} + 2e^{2} - 14e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $1$
4 $[4, 2, w^{2} + w - 7]$ $-1$