# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 9 Level $[9, 9, w - 2]$ Label 3.3.1129.1-9.5-b Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1129.1

Generator $$w$$, with minimal polynomial $$x^{3} - 7x - 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[9, 9, w - 2]$ Label 3.3.1129.1-9.5-b Dimension 3 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut 9x$$ $$\mathstrut -\mathstrut 4$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}0$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 2$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 3$
11 $[11, 11, -w^{2} + 5]$ $-\frac{1}{2}e^{2} + \frac{3}{2}e + 2$
13 $[13, 13, w^{2} - w - 7]$ $-e$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}e^{2} - 2e - 8$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e + 2$
29 $[29, 29, 2w^{2} - 2w - 11]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 2$
31 $[31, 31, w^{2} - 2w - 4]$ $-e$
37 $[37, 37, -2w^{2} + 3w + 7]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 6$
41 $[41, 41, w^{2} - 2]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e - 2$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 2$
61 $[61, 61, w^{2} + w - 10]$ $-3e + 2$
67 $[67, 67, 2w^{2} - w - 11]$ $\phantom{-}e^{2} + e$
73 $[73, 73, -w^{2} - 1]$ $-\frac{3}{2}e^{2} - \frac{3}{2}e + 8$
83 $[83, 83, w^{2} - w - 10]$ $\phantom{-}4e - 4$
89 $[89, 89, -w^{2} + 4w - 2]$ $-e^{2} + 10$
97 $[97, 97, w^{2} - 2w - 7]$ $-e^{2} - 5e + 8$
97 $[97, 97, -w^{2} - 4w - 5]$ $\phantom{-}e^{2} - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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