# Properties

 Label 4.4.15188.1-8.4-e Base field 4.4.15188.1 Weight $[2, 2, 2, 2]$ Level norm $8$ Level $[8, 8, -w^{3} + w^{2} + 7w - 2]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.15188.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[8, 8, -w^{3} + w^{2} + 7w - 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + x - 4$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ $-2e$
11 $[11, 11, -w^{3} + w^{2} + 6w + 1]$ $-2$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}2e + 2$
19 $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ $-2e + 2$
23 $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ $-8$
31 $[31, 31, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}2e - 4$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-2$
43 $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ $\phantom{-}0$
67 $[67, 67, w^{2} - w - 5]$ $\phantom{-}4e + 8$
67 $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ $-2e + 2$
73 $[73, 73, w^{2} + w + 1]$ $-4e - 2$
79 $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ $\phantom{-}2e - 8$
81 $[81, 3, -3]$ $-2e - 6$
83 $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ $\phantom{-}2e - 4$
83 $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ $\phantom{-}4e - 4$
89 $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ $-10$
89 $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ $-4e - 4$
97 $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ $-10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$