# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 3 Level $[3, 3, w + 1]$ Label 3.3.1129.1-3.2-b Dimension 2 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 $[3, 3, w + 1]$ Label 3.3.1129.1-3.2-b Dimension 2 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut 5$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-1$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{2}e - \frac{1}{2}$
8 $[8, 2, 2]$ $-\frac{3}{2}e - \frac{3}{2}$
11 $[11, 11, -w^{2} + 5]$ $-\frac{1}{2}e - \frac{9}{2}$
13 $[13, 13, w^{2} - w - 7]$ $-3$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}e$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}\frac{1}{2}e + \frac{3}{2}$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-\frac{3}{2}e + \frac{7}{2}$
31 $[31, 31, w^{2} - 2w - 4]$ $\phantom{-}1$
37 $[37, 37, -2w^{2} + 3w + 7]$ $-\frac{3}{2}e - \frac{9}{2}$
41 $[41, 41, w^{2} - 2]$ $-\frac{5}{2}e - \frac{9}{2}$
59 $[59, 59, 2w^{2} - 13]$ $-\frac{1}{2}e + \frac{3}{2}$
61 $[61, 61, w^{2} + w - 10]$ $-e$
67 $[67, 67, 2w^{2} - w - 11]$ $-e - 9$
73 $[73, 73, -w^{2} - 1]$ $\phantom{-}\frac{3}{2}e + \frac{15}{2}$
83 $[83, 83, w^{2} - w - 10]$ $-6e - 2$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}4e - 3$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}3e + 11$
97 $[97, 97, -w^{2} - 4w - 5]$ $-1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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