# Properties

 Base field 6.6.1397493.1 Weight [2, 2, 2, 2, 2, 2] Level norm 9 Level $[9, 3, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - 2w + 2]$ Label 6.6.1397493.1-9.1-b Dimension 4 CM no Base change yes

# Related objects

• L-function not available

## Base field 6.6.1397493.1

Generator $$w$$, with minimal polynomial $$x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2, 2, 2] Level $[9, 3, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - 2w + 2]$ Label 6.6.1397493.1-9.1-b Dimension 4 Is CM no Is base change yes Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 54x^{2}$$ $$\mathstrut +\mathstrut 162$$
Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}0$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}e$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $\phantom{-}e$
19 $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ $\phantom{-}2$
19 $[19, 19, w^{2} - w - 1]$ $\phantom{-}2$
37 $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ $-\frac{1}{3}e^{2} + 8$
37 $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ $-\frac{1}{3}e^{2} + 8$
53 $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ $\phantom{-}\frac{1}{9}e^{3} - 5e$
53 $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ $\phantom{-}\frac{1}{9}e^{3} - 5e$
64 $[64, 2, -2]$ $-\frac{1}{3}e^{2} + 17$
71 $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ $-\frac{1}{9}e^{3} + 6e$
71 $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ $-2e$
71 $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ $-\frac{1}{9}e^{3} + 6e$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ $\phantom{-}\frac{1}{3}e^{2} - 4$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ $\phantom{-}\frac{1}{3}e^{2} - 4$
89 $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ $-\frac{2}{9}e^{3} + 9e$
89 $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ $-\frac{2}{9}e^{3} + 9e$
89 $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ $-\frac{1}{9}e^{3} + 7e$
89 $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ $-\frac{1}{9}e^{3} + 7e$
107 $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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