# Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} + 6]$ Label 4.4.17725.1-19.2-b Dimension 12 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 12x^{2} + 13x + 41$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[19, 19, -w^{2} + 6]$ Label 4.4.17725.1-19.2-b Dimension 12 Is CM no Is base change no Parent newspace dimension 32

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{12} + 2x^{11} - 56x^{10} - 97x^{9} + 1130x^{8} + 1649x^{7} - 9868x^{6} - 11978x^{5} + 35133x^{4} + 38543x^{3} - 38960x^{2} - 47327x - 8797$$
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $...$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $...$
19 $[19, 19, w + 1]$ $...$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + 2w + 5]$ $...$
19 $[19, 19, -w + 2]$ $...$
25 $[25, 5, 2w^{2} - 2w - 13]$ $...$
29 $[29, 29, -w^{2} + 9]$ $...$
29 $[29, 29, -w^{2} + 2w + 6]$ $...$
29 $[29, 29, w^{2} - 7]$ $...$
29 $[29, 29, -w^{2} + 2w + 8]$ $...$
31 $[31, 31, -2w^{2} + w + 12]$ $...$
31 $[31, 31, 2w^{2} - 3w - 11]$ $...$
41 $[41, 41, -w]$ $...$
41 $[41, 41, -w + 1]$ $...$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $...$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $...$
61 $[61, 61, 2w^{2} - 3w - 14]$ $...$
61 $[61, 61, 2w^{2} - w - 15]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} + 6]$ $-1$