# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} + w + 1]$ Label 4.4.16997.1-19.1-a Dimension 15 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16997.1

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

## Form

 Weight [2, 2, 2, 2] Level $[19, 19, -w^{2} + w + 1]$ Label 4.4.16997.1-19.1-a Dimension 15 Is CM no Is base change no Parent newspace dimension 34

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{15} + 3x^{14} - 41x^{13} - 126x^{12} + 577x^{11} + 1842x^{10} - 3282x^{9} - 11653x^{8} + 5986x^{7} + 32458x^{6} + 5471x^{5} - 32416x^{4} - 16081x^{3} + 4894x^{2} + 2029x - 307$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $...$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2]$ $...$
13 $[13, 13, -w^{2} + 3]$ $...$
13 $[13, 13, w^{2} - w - 4]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, -w^{2} + w + 1]$ $\phantom{-}1$
23 $[23, 23, -w^{3} + 4w + 2]$ $...$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $...$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $...$
29 $[29, 29, -w + 3]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $...$
37 $[37, 37, w^{3} - 4w - 1]$ $...$
37 $[37, 37, w^{3} - 3w + 1]$ $...$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $...$
59 $[59, 59, w^{2} + w - 4]$ $...$
61 $[61, 61, -2w^{2} + w + 8]$ $...$
73 $[73, 73, -w^{3} + 5w - 1]$ $...$
79 $[79, 79, 2w^{2} + w - 6]$ $...$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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