# Properties

 Label 4.4.6809.1-22.1-e Base field 4.4.6809.1 Weight $[2, 2, 2, 2]$ Level norm $22$ Level $[22, 22, -w^{2} + 3]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.6809.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[22, 22, -w^{2} + 3]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $9$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 2x - 11$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-1$
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}e$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $-\frac{1}{2}e - \frac{5}{2}$
11 $[11, 11, w^{3} - 5w + 1]$ $-1$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $-\frac{1}{2}e + \frac{11}{2}$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}\frac{3}{2}e + \frac{11}{2}$
29 $[29, 29, -w^{2} - w + 3]$ $\phantom{-}0$
31 $[31, 31, -w^{3} + 6w + 2]$ $-\frac{1}{2}e + \frac{3}{2}$
43 $[43, 43, w^{3} - 6w]$ $-e - 4$
47 $[47, 47, 2w^{3} - 9w]$ $\phantom{-}\frac{1}{2}e - \frac{11}{2}$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $\phantom{-}3e$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $\phantom{-}e + 1$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}e + 11$
59 $[59, 59, 3w^{3} - 15w - 5]$ $\phantom{-}e + 11$
71 $[71, 71, w^{3} - 3w - 3]$ $\phantom{-}2e$
81 $[81, 3, -3]$ $\phantom{-}e - 6$
83 $[83, 83, -2w^{3} + 8w + 3]$ $\phantom{-}e + 1$
89 $[89, 89, -2w^{3} + 11w - 2]$ $\phantom{-}3e + 5$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $-2e - 10$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $-2e - 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w + 1]$ $1$
$11$ $[11, 11, w^{3} - 5w + 1]$ $1$