# Properties

 Label 4.4.8768.1-7.1-b Base field 4.4.8768.1 Weight $[2, 2, 2, 2]$ Level norm $7$ Level $[7, 7, w]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.8768.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 6x + 7$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[7, 7, w]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $-2$
7 $[7, 7, w]$ $\phantom{-}1$
7 $[7, 7, -w^{2} + 2w + 1]$ $-4$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}0$
7 $[7, 7, w - 1]$ $-4$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $-4$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}8$
31 $[31, 31, w^{2} - 5]$ $-4$
31 $[31, 31, -w^{2} + 2w + 4]$ $-4$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}12$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}4$
47 $[47, 47, w^{2} - 2w - 5]$ $\phantom{-}8$
47 $[47, 47, w^{2} - 6]$ $\phantom{-}4$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}0$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-8$
79 $[79, 79, -w - 3]$ $\phantom{-}12$
79 $[79, 79, w - 4]$ $\phantom{-}0$
81 $[81, 3, -3]$ $\phantom{-}2$
89 $[89, 89, w^{2} - 3w - 2]$ $-12$
89 $[89, 89, w^{2} + w - 4]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, w]$ $-1$