# Properties

 Label 4.4.10025.1-20.4-a Base field 4.4.10025.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20,10,\frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 9]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.10025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 10x + 20$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20,10,\frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 9]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $13$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $-3$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $-1$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $-8$
19 $[19, 19, w - 1]$ $-2$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $-4$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $\phantom{-}8$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $\phantom{-}10$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $-2$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}4$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $\phantom{-}0$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $-10$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $-6$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $\phantom{-}0$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $\phantom{-}10$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $\phantom{-}16$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $\phantom{-}6$
81 $[81, 3, -3]$ $-8$
89 $[89, 89, w^{3} - 7w + 1]$ $\phantom{-}2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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