# Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, w + 1]$ Label 4.4.17725.1-19.1-d Dimension 3 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 $[19, 19, w + 1]$ Label 4.4.17725.1-19.1-d Dimension 3 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:
$$x^{3}$$ $$\mathstrut -\mathstrut 4x^{2}$$ $$\mathstrut -\mathstrut 12x$$ $$\mathstrut +\mathstrut 36$$
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} + e + 5$
19 $[19, 19, w + 1]$ $-1$
19 $[19, 19, -w^{2} + 6]$ $-\frac{1}{2}e^{2} + 9$
19 $[19, 19, -w^{2} + 2w + 5]$ $-\frac{1}{6}e^{2} + \frac{5}{3}e - 1$
19 $[19, 19, -w + 2]$ $\phantom{-}e - 3$
25 $[25, 5, 2w^{2} - 2w - 13]$ $-\frac{1}{3}e^{2} + \frac{1}{3}e + 1$
29 $[29, 29, -w^{2} + 9]$ $\phantom{-}e - 2$
29 $[29, 29, -w^{2} + 2w + 6]$ $\phantom{-}4$
29 $[29, 29, w^{2} - 7]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + 2$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - 5$
31 $[31, 31, -2w^{2} + w + 12]$ $-\frac{1}{2}e^{2} + 7$
31 $[31, 31, 2w^{2} - 3w - 11]$ $\phantom{-}2e - 2$
41 $[41, 41, -w]$ $\phantom{-}\frac{1}{6}e^{2} + \frac{4}{3}e - 3$
41 $[41, 41, -w + 1]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + 6$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $-\frac{1}{3}e^{2} + \frac{4}{3}e + 2$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{1}{3}e - 14$
61 $[61, 61, 2w^{2} - 3w - 14]$ $-\frac{1}{3}e^{2} + \frac{7}{3}e + 2$
61 $[61, 61, 2w^{2} - w - 15]$ $-\frac{2}{3}e^{2} + \frac{5}{3}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, w + 1]$ $1$