# Properties

 Label 4.4.13824.1-9.1-a Base field 4.4.13824.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, -w^{2} + 3]$ Dimension $1$ CM no Base change no

# Related objects

## 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: $1$ CM: no Base change: no Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}0$
3 $[3, 3, w^{2} - w - 3]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + w + 1]$ $-4$
11 $[11, 11, -w^{2} - w + 1]$ $\phantom{-}4$
13 $[13, 13, w^{3} - 4w + 1]$ $\phantom{-}0$
13 $[13, 13, -w^{3} + 4w + 1]$ $\phantom{-}0$
25 $[25, 5, -w^{2} - 2w + 1]$ $-4$
25 $[25, 5, w^{2} - 2w - 1]$ $-4$
37 $[37, 37, w^{3} - 3w - 1]$ $-6$
37 $[37, 37, w^{3} - 3w + 1]$ $-6$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}4$
59 $[59, 59, -w^{2} - w + 5]$ $-4$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $-2$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $-2$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}4$
73 $[73, 73, 2w - 1]$ $\phantom{-}4$
73 $[73, 73, -2w - 1]$ $\phantom{-}4$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}4$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $-4$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $\phantom{-}4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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