# Properties

 Label 4.4.13676.1-8.2-a Base field 4.4.13676.1 Weight $[2, 2, 2, 2]$ Level norm $8$ Level $[8, 4, -w^{3} + 5w - 2]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13676.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} + 7x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[8, 4, -w^{3} + 5w - 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 5$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} - w + 3]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 5w + 1]$ $-1$
11 $[11, 11, -w^{3} + 6w - 2]$ $-e - 3$
13 $[13, 13, -w^{2} + 4]$ $\phantom{-}e - 2$
17 $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $-e$
37 $[37, 37, w^{3} + w^{2} - 6w - 3]$ $-3e$
37 $[37, 37, -w^{3} + 6w - 4]$ $-2e - 5$
41 $[41, 41, -w^{3} + 5w - 5]$ $\phantom{-}2e - 1$
43 $[43, 43, w^{3} - 4w + 4]$ $\phantom{-}e - 5$
43 $[43, 43, -2w^{3} + 11w - 2]$ $\phantom{-}e + 9$
47 $[47, 47, -2w^{3} - w^{2} + 12w]$ $-e + 7$
47 $[47, 47, 2w - 1]$ $-4e + 2$
61 $[61, 61, -w^{3} + w^{2} + 6w - 5]$ $-2e - 8$
71 $[71, 71, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}6e$
71 $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ $\phantom{-}e + 3$
79 $[79, 79, w^{3} + w^{2} - 6w - 5]$ $-4e + 2$
81 $[81, 3, -3]$ $\phantom{-}e - 10$
83 $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ $\phantom{-}3e - 5$
97 $[97, 97, w^{3} + w^{2} - 6w + 1]$ $\phantom{-}4e + 3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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