# Properties

 Label 4.4.12725.1-19.2-b Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,w^{2} - 6]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19,19,w^{2} - 6]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{2} - 5$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $-\frac{3}{2}e - \frac{1}{2}$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1}{2}e + \frac{1}{2}$
11 $[11, 11, w - 2]$ $\phantom{-}\frac{1}{2}e - \frac{5}{2}$
16 $[16, 2, 2]$ $-\frac{3}{2}e - \frac{3}{2}$
19 $[19, 19, w^{2} - 2w - 5]$ $\phantom{-}\frac{3}{2}e - \frac{5}{2}$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}1$
25 $[25, 5, -2w^{2} + 2w + 11]$ $-\frac{3}{2}e - \frac{9}{2}$
29 $[29, 29, w]$ $\phantom{-}\frac{5}{2}e + \frac{1}{2}$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}e$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-\frac{5}{2}e + \frac{5}{2}$
29 $[29, 29, w - 1]$ $\phantom{-}\frac{5}{2}e - \frac{7}{2}$
31 $[31, 31, w^{3} - 6w - 6]$ $\phantom{-}\frac{1}{2}e - \frac{11}{2}$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $-\frac{7}{2}e + \frac{5}{2}$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $\phantom{-}e + 3$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $\phantom{-}\frac{3}{2}e + \frac{15}{2}$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $-3e - 2$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}2e + 1$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $-2e + 3$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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