# Properties

 Base field 4.4.8768.1 Weight [2, 2, 2, 2] Level norm 28 Level $[28,14,w^{3} - 2w^{2} - 2w + 3]$ Label 4.4.8768.1-28.4-d 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 $[28,14,w^{3} - 2w^{2} - 2w + 3]$ Label 4.4.8768.1-28.4-d Dimension 1 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}1$
7 $[7, 7, w]$ $\phantom{-}3$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}0$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}3$
7 $[7, 7, w - 1]$ $\phantom{-}1$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}8$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $-4$
31 $[31, 31, w^{2} - 5]$ $-11$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}10$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $-10$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $-2$
47 $[47, 47, w^{2} - 2w - 5]$ $-3$
47 $[47, 47, w^{2} - 6]$ $-6$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}6$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}7$
79 $[79, 79, -w - 3]$ $\phantom{-}14$
79 $[79, 79, w - 4]$ $\phantom{-}5$
81 $[81, 3, -3]$ $-5$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}6$
89 $[89, 89, w^{2} + w - 4]$ $\phantom{-}2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4,2,-w^{2} + w + 3]$ $-1$
7 $[7,7,-w + 1]$ $-1$