# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 9 Level $[9, 9, w + 3]$ Label 3.3.1129.1-9.4-f 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 $[9, 9, w + 3]$ Label 3.3.1129.1-9.4-f Dimension 4 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:
$$x^{4} - 6x^{2} + 2$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-e$
8 $[8, 2, 2]$ $-e^{2} + 1$
11 $[11, 11, -w^{2} + 5]$ $-e^{3} + 4e$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}2e^{3} - 10e$
17 $[17, 17, -w^{2} + w + 4]$ $-2e^{3} + 11e$
19 $[19, 19, -w^{2} - w + 4]$ $-2$
29 $[29, 29, 2w^{2} - 2w - 11]$ $\phantom{-}3e^{3} - 15e$
31 $[31, 31, w^{2} - 2w - 4]$ $-2e^{3} + 13e$
37 $[37, 37, -2w^{2} + 3w + 7]$ $-e$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}e^{3} - 4e$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}e^{2} - 10$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}3e^{2} - 14$
67 $[67, 67, 2w^{2} - w - 11]$ $\phantom{-}3e^{3} - 20e$
73 $[73, 73, -w^{2} - 1]$ $-4e^{2} + 8$
83 $[83, 83, w^{2} - w - 10]$ $-2e^{2} + 8$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}3e^{2} - 12$
97 $[97, 97, w^{2} - 2w - 7]$ $-4e^{3} + 18e$
97 $[97, 97, -w^{2} - 4w - 5]$ $-16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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