# Properties

 Label 4.4.19025.1-20.2-d Base field 4.4.19025.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, -w^{2} + 2w + 5]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.19025.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 13x^{2} + 14x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, -w^{2} + 2w + 5]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $35$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + x - 5$$
Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $\phantom{-}e - 1$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $-1$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $-e$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $-5$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $\phantom{-}5$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $-2e + 5$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $\phantom{-}0$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $-e - 5$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $-e$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $\phantom{-}e$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $-e - 7$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $\phantom{-}13$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $\phantom{-}e - 2$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $-4e - 2$
81 $[81, 3, -3]$ $\phantom{-}5$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $\phantom{-}4e - 5$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $\phantom{-}5e + 5$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $-4e - 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + 7]$ $-1$
$5$ $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $1$