# Properties

 Label 4.4.17609.1-22.1-d Base field 4.4.17609.1 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 4.4.17609.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 10x - 1$$; narrow class number $$2$$ 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: $32$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 4x + 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 6w - 2]$ $\phantom{-}e + 2$
8 $[8, 2, w^{3} - 7w + 3]$ $-e$
11 $[11, 11, -w^{3} + 6w - 4]$ $-1$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}2e + 1$
17 $[17, 17, -w^{2} - w + 3]$ $-2e - 5$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $-2e - 2$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $\phantom{-}4$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}2e$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $-2e + 4$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $-2e - 13$
59 $[59, 59, -2w^{3} + 13w - 6]$ $-e - 8$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $-4e - 14$
59 $[59, 59, w^{2} + w - 1]$ $-2e - 6$
59 $[59, 59, w^{2} + 2w - 6]$ $-4e - 10$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $\phantom{-}6e + 9$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}3e + 2$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $-2e - 1$
81 $[81, 3, -3]$ $\phantom{-}2e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $-1$
$11$ $[11, 11, -w^{3} + 6w - 4]$ $1$