# Properties

 Base field 4.4.6125.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19,19,-w^{3} - w^{2} + 5w + 3]$ Label 4.4.6125.1-19.4-b Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.6125.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 9x^{2} + 9x + 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[19,19,-w^{3} - w^{2} + 5w + 3]$ Label 4.4.6125.1-19.4-b Dimension 2 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 4x$$ $$\mathstrut +\mathstrut 1$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $\phantom{-}e$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $\phantom{-}2$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $\phantom{-}2e + 3$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $-e$
11 $[11, 11, w - 1]$ $-4$
16 $[16, 2, 2]$ $-e - 4$
19 $[19, 19, -w^{2} + 4]$ $-2e - 8$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $-2e - 5$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $\phantom{-}e - 2$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $\phantom{-}1$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $\phantom{-}4$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $\phantom{-}4e + 2$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $\phantom{-}2e - 2$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $-e - 2$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $-4e - 8$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $\phantom{-}4e + 14$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $-2e + 2$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $-e - 2$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $-2e + 2$
81 $[81, 3, -3]$ $\phantom{-}4e + 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,-w^{3} - w^{2} + 5w + 3]$ $-1$