# Properties

 Base field 6.6.1397493.1 Weight [2, 2, 2, 2, 2, 2] Level norm 19 Level $[19,19,-w^{2} + w + 1]$ Label 6.6.1397493.1-19.2-d Dimension 14 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 $[19,19,-w^{2} + w + 1]$ Label 6.6.1397493.1-19.2-d Dimension 14 Is CM no Is base change no Parent newspace dimension 18

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{14}$$ $$\mathstrut -\mathstrut 180x^{12}$$ $$\mathstrut +\mathstrut 12844x^{10}$$ $$\mathstrut -\mathstrut 462728x^{8}$$ $$\mathstrut +\mathstrut 8881472x^{6}$$ $$\mathstrut -\mathstrut 88352640x^{4}$$ $$\mathstrut +\mathstrut 415220096x^{2}$$ $$\mathstrut -\mathstrut 694863104$$
Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $...$
17 $[17, 17, -w^{2} + 2w + 1]$ $...$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $\phantom{-}e$
19 $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ $...$
19 $[19, 19, w^{2} - w - 1]$ $-1$
37 $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ $...$
37 $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ $...$
53 $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ $...$
53 $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ $...$
64 $[64, 2, -2]$ $...$
71 $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ $...$
71 $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ $...$
71 $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ $...$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ $...$
73 $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ $...$
89 $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ $...$
89 $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ $...$
89 $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ $...$
89 $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ $...$
107 $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,-w^{2} + w + 1]$ $1$