# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 3 Level $[3, 3, w + 2]$ Label 3.3.1129.1-3.3-a Dimension 4 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 $[3, 3, w + 2]$ Label 3.3.1129.1-3.3-a Dimension 4 Is CM no Is base change no Parent newspace dimension 8

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 4x^{3}$$ $$\mathstrut -\mathstrut 2x^{2}$$ $$\mathstrut +\mathstrut 12x$$ $$\mathstrut +\mathstrut 6$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e^{2} - 2e - 4$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}1$
8 $[8, 2, 2]$ $-e^{3} + 3e^{2} + 2e - 5$
11 $[11, 11, -w^{2} + 5]$ $-e^{3} + 4e^{2} - e - 6$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}2e^{2} - 3e - 6$
17 $[17, 17, -w^{2} + w + 4]$ $-2e + 4$
19 $[19, 19, -w^{2} - w + 4]$ $-2$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-2e^{3} + 4e^{2} + 8e - 4$
31 $[31, 31, w^{2} - 2w - 4]$ $-e^{3} + 4e^{2} - e - 8$
37 $[37, 37, -2w^{2} + 3w + 7]$ $\phantom{-}2e^{3} - 8e^{2} + e + 12$
41 $[41, 41, w^{2} - 2]$ $-4e^{2} + 6e + 16$
59 $[59, 59, 2w^{2} - 13]$ $-6$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}2e^{3} - 5e^{2} - 10e + 10$
67 $[67, 67, 2w^{2} - w - 11]$ $-e^{3} + 4e^{2} + e - 2$
73 $[73, 73, -w^{2} - 1]$ $-2e^{3} + 6e^{2} - 4$
83 $[83, 83, w^{2} - w - 10]$ $-e^{2} + 4e - 4$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}2e^{3} - 8e^{2} + 4e + 8$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}e^{3} - 8e^{2} + 9e + 16$
97 $[97, 97, -w^{2} - 4w - 5]$ $\phantom{-}4e - 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 2]$ $-1$