# Properties

 Label 4.4.19025.1-20.2-e Base field 4.4.19025.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, -w^{2} + 2w + 5]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## 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: $4$ 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:

 $$x^{4} - 11x^{2} + 9x + 9$$
Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $\phantom{-}\frac{2}{3}e^{3} + e^{2} - \frac{16}{3}e - 1$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $-1$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $-e^{3} - 2e^{2} + 7e + 4$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $-\frac{1}{3}e^{3} + \frac{8}{3}e - 1$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $-\frac{2}{3}e^{3} - e^{2} + \frac{16}{3}e - 1$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $\phantom{-}e^{3} + 2e^{2} - 6e - 5$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $\phantom{-}\frac{1}{3}e^{3} - e^{2} - \frac{20}{3}e + 8$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $\phantom{-}\frac{2}{3}e^{3} + 2e^{2} - \frac{19}{3}e - 5$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $-e^{3} - 4e^{2} + 5e + 14$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $\phantom{-}\frac{7}{3}e^{3} + 4e^{2} - \frac{56}{3}e - 3$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e - 5$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $\phantom{-}e^{2} + e - 12$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $-\frac{5}{3}e^{3} - 4e^{2} + \frac{28}{3}e + 7$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $\phantom{-}\frac{1}{3}e^{3} + e^{2} - \frac{8}{3}e - 8$
81 $[81, 3, -3]$ $\phantom{-}\frac{5}{3}e^{3} + 4e^{2} - \frac{40}{3}e - 9$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $\phantom{-}\frac{5}{3}e^{3} + 4e^{2} - \frac{28}{3}e - 9$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $-\frac{10}{3}e^{3} - 6e^{2} + \frac{65}{3}e + 11$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $\phantom{-}\frac{4}{3}e^{3} + 4e^{2} - \frac{20}{3}e - 22$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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