# Properties

 Label 4.4.13824.1-22.1-b Base field 4.4.13824.1 Weight $[2, 2, 2, 2]$ Level norm $22$ Level $[22, 22, -w^{3} + w^{2} + 3w - 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13824.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[22, 22, -w^{3} + w^{2} + 3w - 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $26$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 6x^{3} - 6x^{2} - 45x + 27$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $-1$
3 $[3, 3, w^{2} - w - 3]$ $-\frac{1}{3}e^{2} - e + 3$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}e$
11 $[11, 11, -w^{2} - w + 1]$ $\phantom{-}1$
13 $[13, 13, w^{3} - 4w + 1]$ $-\frac{1}{9}e^{3} - \frac{1}{3}e^{2} + \frac{5}{3}e$
13 $[13, 13, -w^{3} + 4w + 1]$ $\phantom{-}\frac{2}{9}e^{3} + \frac{2}{3}e^{2} - \frac{7}{3}e - 3$
25 $[25, 5, -w^{2} - 2w + 1]$ $\phantom{-}\frac{2}{9}e^{3} + \frac{1}{3}e^{2} - \frac{13}{3}e$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}\frac{2}{9}e^{3} + \frac{4}{3}e^{2} + \frac{2}{3}e - 9$
37 $[37, 37, w^{3} - 3w - 1]$ $-\frac{4}{9}e^{3} - \frac{7}{3}e^{2} + \frac{5}{3}e + 6$
37 $[37, 37, w^{3} - 3w + 1]$ $\phantom{-}\frac{2}{9}e^{3} + e^{2} - \frac{4}{3}e - 6$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}\frac{1}{3}e^{2} - e$
59 $[59, 59, -w^{2} - w + 5]$ $\phantom{-}e^{2} + e - 12$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $-\frac{1}{9}e^{3} - e^{2} + \frac{2}{3}e + 3$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $-\frac{1}{9}e^{3} + e^{2} + \frac{14}{3}e - 15$
73 $[73, 73, 2w^{2} - w - 5]$ $-\frac{1}{3}e^{3} - 2e^{2} + 2e + 5$
73 $[73, 73, 2w - 1]$ $\phantom{-}\frac{2}{9}e^{3} + \frac{7}{3}e^{2} + \frac{8}{3}e - 15$
73 $[73, 73, -2w - 1]$ $-\frac{4}{9}e^{3} - \frac{5}{3}e^{2} + \frac{17}{3}e + 9$
73 $[73, 73, 2w^{2} + w - 5]$ $-e^{3} - \frac{14}{3}e^{2} + 4e + 14$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $\phantom{-}\frac{1}{3}e^{2} - 2e - 6$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{8}{3}e^{2} + 3e - 18$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-w^{2}+w+2]$ $1$
$11$ $[11,11,-w^{2}-w+1]$ $-1$