# Properties

 Base field 6.6.1397493.1 Weight [2, 2, 2, 2, 2, 2] Level norm 17 Level $[17,17,w^{3} - w^{2} - 4w]$ Label 6.6.1397493.1-17.2-d Dimension 3 CM no Base change no

# 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 $[17,17,w^{3} - w^{2} - 4w]$ Label 6.6.1397493.1-17.2-d Dimension 3 Is CM no Is base change no Parent newspace dimension 10

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} + 3x^{2} - 3$$
Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}e$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}3e^{2} + 3e - 9$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $\phantom{-}1$
19 $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ $\phantom{-}e^{2} - 4$
19 $[19, 19, w^{2} - w - 1]$ $-2e^{2} - 3e + 5$
37 $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ $-5e^{2} - 6e + 8$
37 $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ $\phantom{-}4e^{2} + 3e - 10$
53 $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ $\phantom{-}6e + 9$
53 $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ $\phantom{-}3e^{2} + 6e - 9$
64 $[64, 2, -2]$ $-5e^{2} - 9e + 8$
71 $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ $\phantom{-}3e^{2} + 6e - 9$
71 $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ $-3e$
71 $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ $-3e^{2} - 3e$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ $-2e^{2} + 3e + 11$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ $\phantom{-}e^{2} + 2$
89 $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ $\phantom{-}3e^{2} + 3e - 9$
89 $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ $\phantom{-}6e^{2} + 9e - 9$
89 $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ $-6e^{2} - 9e$
89 $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ $\phantom{-}3e^{2} + 6e$
107 $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ $-12e^{2} - 21e + 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17,17,w^{3} - w^{2} - 4w]$ $-1$