# Properties

 Label 4.4.7168.1-9.2-a Base field 4.4.7168.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9,3,w^{2} - w - 1]$ Dimension $2$ CM no Base change no

# Related objects

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## Base field 4.4.7168.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} + 7$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9,3,w^{2} - w - 1]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
7 $[7, 7, w]$ $-e + 1$
9 $[9, 3, w^{2} + w - 1]$ $\phantom{-}e + 2$
9 $[9, 3, w^{2} - w - 1]$ $-1$
17 $[17, 17, -w^{3} + 3w - 1]$ $\phantom{-}3$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}3$
23 $[23, 23, -w^{3} - w^{2} + 3w + 4]$ $-1$
23 $[23, 23, w^{3} - w^{2} - 3w + 4]$ $-1$
41 $[41, 41, w^{3} - w^{2} - 2w + 3]$ $-7e + 8$
41 $[41, 41, -w^{3} - w^{2} + 2w + 3]$ $\phantom{-}5e - 3$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}4e - 7$
71 $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ $-2e + 8$
71 $[71, 71, -2w^{2} - 2w + 1]$ $\phantom{-}10e - 3$
73 $[73, 73, w^{2} - 2w - 2]$ $-13e + 8$
73 $[73, 73, w^{2} + 2w - 2]$ $\phantom{-}9$
79 $[79, 79, w^{3} - w^{2} - 5w + 2]$ $-4e - 3$
79 $[79, 79, -w^{3} - w^{2} + 5w + 2]$ $-3e + 9$
89 $[89, 89, 2w - 1]$ $-3e - 1$
89 $[89, 89, -2w - 1]$ $\phantom{-}10e$
97 $[97, 97, -w^{3} + w^{2} + 4w - 1]$ $-3e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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