# Properties

 Label 4.4.13824.1-9.1-d Base field 4.4.13824.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, -w^{2} + 3]$ Dimension $8$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.13824.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, -w^{2} + 3]$ Dimension: $8$ CM: no Base change: yes Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{8} - 16x^{6} + 82x^{4} - 152x^{2} + 72$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 3]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + w + 1]$ $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{27}{2}e^{3} + 13e$
11 $[11, 11, -w^{2} - w + 1]$ $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{27}{2}e^{3} + 13e$
13 $[13, 13, w^{3} - 4w + 1]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + \frac{25}{2}e^{2} - 7$
13 $[13, 13, -w^{3} + 4w + 1]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + \frac{25}{2}e^{2} - 7$
25 $[25, 5, -w^{2} - 2w + 1]$ $-\frac{3}{4}e^{6} + \frac{19}{2}e^{4} - \frac{63}{2}e^{2} + 23$
25 $[25, 5, w^{2} - 2w - 1]$ $-\frac{3}{4}e^{6} + \frac{19}{2}e^{4} - \frac{63}{2}e^{2} + 23$
37 $[37, 37, w^{3} - 3w - 1]$ $-2e^{2} + 8$
37 $[37, 37, w^{3} - 3w + 1]$ $-2e^{2} + 8$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + 17e^{3} - 4e$
59 $[59, 59, -w^{2} - w + 5]$ $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + 17e^{3} - 4e$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $-\frac{1}{2}e^{6} + 5e^{4} - 9e^{2} - 4$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $-\frac{1}{2}e^{6} + 5e^{4} - 9e^{2} - 4$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{5}{2}e^{2} + 11$
73 $[73, 73, 2w - 1]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{19}{2}e^{4} + \frac{63}{2}e^{2} - 19$
73 $[73, 73, -2w - 1]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{19}{2}e^{4} + \frac{63}{2}e^{2} - 19$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{5}{2}e^{2} + 11$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{3}{2}e^{3} - 17e$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{3}{2}e^{3} - 17e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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