# Properties

 Label 4.4.19796.1-8.3-a Base field 4.4.19796.1 Weight $[2, 2, 2, 2]$ Level norm $8$ Level $[8, 4, -w^{2} + w + 4]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19796.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + x + 8$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[8, 4, -w^{2} + w + 4]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 13x^{2} + 32$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}0$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $\phantom{-}1$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $-\frac{1}{4}e^{3} + \frac{5}{4}e$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $-\frac{3}{4}e^{3} + \frac{23}{4}e$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $-e^{2} + 8$
31 $[31, 31, -w^{2} + w + 1]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{3}{4}e$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}\frac{5}{4}e^{3} - \frac{37}{4}e$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $-\frac{1}{4}e^{3} + \frac{5}{4}e$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $-3e^{2} + 20$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}3e^{2} - 16$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $-\frac{1}{2}e^{3} + \frac{17}{2}e$
61 $[61, 61, 2w^{2} - 7]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{4}e$
71 $[71, 71, w^{2} - 3w - 5]$ $\phantom{-}2e^{2} - 8$
73 $[73, 73, 2w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{25}{2}e$
79 $[79, 79, 2w^{2} - 5]$ $\phantom{-}e^{2} + 4$
81 $[81, 3, -3]$ $\phantom{-}2e^{2} - 22$
101 $[101, 101, 2w^{2} - 4w - 9]$ $\phantom{-}\frac{3}{4}e^{3} - \frac{23}{4}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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