# Properties

 Label 4.4.17428.1-9.1-g Base field 4.4.17428.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 9, w^{2} + w - 3]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.17428.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} + 4x + 6$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 9, w^{2} + w - 3]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $20$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 2x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e + 1$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + w + 3]$ $\phantom{-}0$
27 $[27, 3, -w^{3} - 2w^{2} + 3w + 5]$ $\phantom{-}4e + 4$
29 $[29, 29, w^{3} + w^{2} - 2w - 1]$ $-4e - 8$
31 $[31, 31, -w^{2} - w + 1]$ $\phantom{-}4$
31 $[31, 31, w^{3} - 2w^{2} - 5w + 7]$ $\phantom{-}4$
37 $[37, 37, -w^{3} + 3w + 1]$ $-4$
41 $[41, 41, -w^{2} + w + 5]$ $-4e - 4$
41 $[41, 41, -w^{3} + w^{2} + 4w - 1]$ $-4e - 8$
43 $[43, 43, -2w - 1]$ $\phantom{-}4e + 6$
47 $[47, 47, w^{2} + w - 5]$ $-4e - 2$
47 $[47, 47, 2w^{3} - 3w^{2} - 9w + 11]$ $\phantom{-}0$
53 $[53, 53, w^{3} + 2w^{2} - 5w - 5]$ $-4e - 8$
59 $[59, 59, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}4e + 4$
59 $[59, 59, w^{3} + w^{2} - 4w - 5]$ $\phantom{-}8e + 12$
71 $[71, 71, 2w^{3} - 4w^{2} - 10w + 19]$ $\phantom{-}8e + 4$
71 $[71, 71, w^{2} + 3w + 1]$ $-12$
73 $[73, 73, w^{3} - 5w + 1]$ $-12$
89 $[89, 89, -4w^{3} + 7w^{2} + 19w - 29]$ $-4e - 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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