# Properties

 Label 4.4.7168.1-32.1-b Base field 4.4.7168.1 Weight $[2, 2, 2, 2]$ Level norm $32$ Level $[32, 4, 2w + 2]$ Dimension $1$ CM no Base change no

# Related objects

## 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: $[32, 4, 2w + 2]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}0$
7 $[7, 7, w]$ $-4$
9 $[9, 3, w^{2} + w - 1]$ $\phantom{-}4$
9 $[9, 3, w^{2} - w - 1]$ $-4$
17 $[17, 17, -w^{3} + 3w - 1]$ $\phantom{-}4$
17 $[17, 17, w^{3} - 3w - 1]$ $-4$
23 $[23, 23, -w^{3} - w^{2} + 3w + 4]$ $-4$
23 $[23, 23, w^{3} - w^{2} - 3w + 4]$ $\phantom{-}4$
41 $[41, 41, w^{3} - w^{2} - 2w + 3]$ $-2$
41 $[41, 41, -w^{3} - w^{2} + 2w + 3]$ $-2$
49 $[49, 7, w^{2} - 6]$ $-2$
71 $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ $-4$
71 $[71, 71, -2w^{2} - 2w + 1]$ $-4$
73 $[73, 73, w^{2} - 2w - 2]$ $\phantom{-}4$
73 $[73, 73, w^{2} + 2w - 2]$ $-4$
79 $[79, 79, w^{3} - w^{2} - 5w + 2]$ $-8$
79 $[79, 79, -w^{3} - w^{2} + 5w + 2]$ $-8$
89 $[89, 89, 2w - 1]$ $-12$
89 $[89, 89, -2w - 1]$ $\phantom{-}12$
97 $[97, 97, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,w+1]$ $-1$