# Properties

 Label 4.4.12725.1-19.2-d Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,w^{2} - 6]$ Dimension $4$ 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: $4$ 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:

 $$x^{4} + 5x^{3} - 14x^{2} - 68x + 8$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{3}{8}e^{2} - \frac{3}{2}e - \frac{7}{2}$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $-\frac{3}{16}e^{3} - \frac{9}{16}e^{2} + \frac{11}{4}e + \frac{17}{4}$
11 $[11, 11, w - 2]$ $\phantom{-}\frac{1}{4}e^{2} + \frac{1}{4}e - \frac{11}{2}$
16 $[16, 2, 2]$ $-\frac{1}{16}e^{3} + \frac{1}{16}e^{2} + \frac{1}{2}e - \frac{15}{4}$
19 $[19, 19, w^{2} - 2w - 5]$ $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{13}{4}e + \frac{7}{2}$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}1$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}\frac{1}{16}e^{3} - \frac{1}{16}e^{2} - \frac{3}{2}e + \frac{3}{4}$
29 $[29, 29, w]$ $\phantom{-}\frac{1}{16}e^{3} - \frac{5}{16}e^{2} - \frac{7}{4}e - \frac{3}{4}$
29 $[29, 29, 2w^{2} - w - 10]$ $-e - 3$
29 $[29, 29, -2w^{2} + 3w + 9]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{1}{8}e^{2} - \frac{11}{4}e - 1$
29 $[29, 29, w - 1]$ $\phantom{-}\frac{1}{4}e^{2} + \frac{5}{4}e - \frac{5}{2}$
31 $[31, 31, w^{3} - 6w - 6]$ $\phantom{-}2$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $-\frac{1}{8}e^{3} + \frac{1}{8}e^{2} + 4e + \frac{1}{2}$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{4}e^{2} - 5e + 4$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $-\frac{1}{16}e^{3} + \frac{9}{16}e^{2} - \frac{43}{4}$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $-\frac{3}{16}e^{3} - \frac{17}{16}e^{2} + \frac{5}{4}e + \frac{29}{4}$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}\frac{9}{16}e^{3} + \frac{27}{16}e^{2} - \frac{33}{4}e - \frac{51}{4}$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}\frac{1}{16}e^{3} - \frac{9}{16}e^{2} - e + \frac{27}{4}$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{7}{16}e^{3} + \frac{5}{16}e^{2} - \frac{31}{4}e + \frac{15}{4}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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