# Properties

 Base field 4.4.2777.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.2777.1-16.1-b Dimension 1 CM no Base change no

# Related objects

## Base field 4.4.2777.1

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

## Form

 Weight [2, 2, 2, 2] Level $[16, 2, 2]$ Label 4.4.2777.1-16.1-b Dimension 1 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
8 $[8, 2, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 2w^{2} - 2w + 1]$ $-2$
23 $[23, 23, -w^{3} + 4w + 1]$ $-4$
23 $[23, 23, -w^{2} + 2w + 3]$ $-4$
31 $[31, 31, w^{3} - 2w^{2} - w + 3]$ $\phantom{-}4$
37 $[37, 37, -w^{3} + 3w + 3]$ $\phantom{-}10$
37 $[37, 37, -2w^{3} + 3w^{2} + 6w - 3]$ $\phantom{-}10$
41 $[41, 41, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}0$
41 $[41, 41, -2w^{3} + 2w^{2} + 6w - 1]$ $\phantom{-}0$
43 $[43, 43, -w^{2} + w + 5]$ $\phantom{-}2$
47 $[47, 47, 2w^{2} - 3w - 5]$ $-8$
53 $[53, 53, -w^{3} + 3w^{2} + w - 7]$ $-2$
53 $[53, 53, -2w^{2} + 2w + 5]$ $-2$
59 $[59, 59, 2w^{2} - w - 7]$ $-10$
61 $[61, 61, 2w^{2} - w - 3]$ $\phantom{-}6$
61 $[61, 61, 2w^{2} - w - 5]$ $\phantom{-}6$
67 $[67, 67, 2w^{3} - 2w^{2} - 7w + 3]$ $-2$
67 $[67, 67, 2w^{3} - 2w^{2} - 7w - 1]$ $-2$
71 $[71, 71, 2w^{3} - 4w^{2} - 4w + 7]$ $-12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
8 $[8, 2, -w^{3} + w^{2} + 4w - 1]$ $-1$