# Properties

 Label 4.4.8112.1-9.2-b Base field 4.4.8112.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, -w^{2} + 2]$ Dimension $4$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.8112.1

Generator $$w$$, with minimal polynomial $$x^{4} - 5x^{2} + 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, -w^{2} + 2]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 10x^{2} + 8$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, w^{2} - w - 1]$ $-\frac{1}{4}e^{3} + \frac{7}{2}e$
9 $[9, 3, -w^{2} + 2]$ $-1$
13 $[13, 13, w^{3} - 4w + 2]$ $-\frac{1}{2}e^{3} + 4e$
13 $[13, 13, -w^{3} + 4w + 2]$ $-\frac{1}{2}e^{3} + 4e$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - 5e$
17 $[17, 17, -w^{3} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - 5e$
29 $[29, 29, w^{3} + w^{2} - 4w - 2]$ $-e^{3} + 6e$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $-e^{3} + 6e$
43 $[43, 43, w^{2} + w - 4]$ $-2e^{2} + 8$
43 $[43, 43, w^{2} - w - 4]$ $-2e^{2} + 8$
53 $[53, 53, w^{3} - 2w - 2]$ $\phantom{-}3e^{2} - 16$
53 $[53, 53, -w^{3} + 2w - 2]$ $\phantom{-}3e^{2} - 16$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-e^{3} + 9e$
79 $[79, 79, -w^{3} - w^{2} + 4w + 1]$ $-e^{3} + 9e$
101 $[101, 101, -w^{3} + w^{2} + 3w - 5]$ $-e^{2} + 12$
101 $[101, 101, w^{3} + w^{2} - 3w - 5]$ $-e^{2} + 12$
103 $[103, 103, 2w^{2} - w - 4]$ $\phantom{-}3e^{2} - 20$
103 $[103, 103, 2w^{2} + w - 4]$ $\phantom{-}3e^{2} - 20$
107 $[107, 107, 2w^{2} + w - 5]$ $-e^{2} + 18$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, -w^{2} + 2]$ $1$