# Properties

 Label 4.4.16609.1-8.2-d Base field 4.4.16609.1 Weight $[2, 2, 2, 2]$ Level norm $8$ Level $[8, 8, -w^{3} + w^{2} + 5w - 5]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16609.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} - x + 9$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[8, 8, -w^{3} + w^{2} + 5w - 5]$ Dimension: $4$ 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:

 $$x^{4} + 3x^{3} - 8x^{2} - 9x + 9$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $\phantom{-}0$
3 $[3, 3, -w^{2} + w + 3]$ $-\frac{1}{3}e^{3} - e^{2} + \frac{5}{3}e + 1$
5 $[5, 5, w^{2} - 4]$ $\phantom{-}e$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{7}{3}e + \frac{3}{2}$
17 $[17, 17, -w^{2} + w + 5]$ $\phantom{-}\frac{1}{6}e^{3} + e^{2} + \frac{2}{3}e - \frac{9}{2}$
27 $[27, 3, -w^{3} + 4w - 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - e - \frac{19}{2}$
29 $[29, 29, -w^{3} + 4w + 2]$ $-\frac{1}{6}e^{3} + e^{2} + \frac{13}{3}e - \frac{9}{2}$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $-\frac{2}{3}e^{3} - 3e^{2} + \frac{10}{3}e + 10$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} - \frac{2}{3}e - 8$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $-\frac{1}{3}e^{3} - 2e^{2} - \frac{7}{3}e + 4$
61 $[61, 61, w^{2} - 2w - 2]$ $\phantom{-}e^{3} + 4e^{2} - 2e - 6$
61 $[61, 61, 2w^{2} - w - 8]$ $-\frac{5}{6}e^{3} - 2e^{2} + \frac{14}{3}e - \frac{5}{2}$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $-2e^{2} - 3e + 9$
73 $[73, 73, -w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - 5e - \frac{15}{2}$
79 $[79, 79, w^{2} - 2w - 4]$ $\phantom{-}\frac{5}{3}e^{3} + 6e^{2} - \frac{28}{3}e - 13$
89 $[89, 89, w^{2} + w - 5]$ $-\frac{3}{2}e^{3} - 5e^{2} + 7e + \frac{7}{2}$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $\phantom{-}\frac{7}{6}e^{3} + 2e^{2} - \frac{37}{3}e - \frac{3}{2}$
89 $[89, 89, w^{3} - 5w - 5]$ $-e^{2} - 6e + 4$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $-e^{3} - e^{2} + 9e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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