# Properties

 Label 4.4.9248.1-16.1-b Base field 4.4.9248.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field 4.4.9248.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $2$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + w + 3]$ $-4$
13 $[13, 13, w^{2} + w - 3]$ $-4$
19 $[19, 19, -w^{3} + 3w + 1]$ $-4$
19 $[19, 19, -w^{3} + 3w - 1]$ $-4$
43 $[43, 43, -w^{2} + w - 1]$ $\phantom{-}8$
43 $[43, 43, w^{2} + w + 1]$ $\phantom{-}8$
49 $[49, 7, w^{3} + w^{2} - 6w - 3]$ $-4$
49 $[49, 7, w^{3} - w^{2} - 6w + 3]$ $-4$
53 $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ $-6$
53 $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ $-6$
59 $[59, 59, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}0$
59 $[59, 59, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}0$
67 $[67, 67, 3w^{3} - 13w + 1]$ $-4$
67 $[67, 67, -w^{3} + w^{2} + 6w - 5]$ $-4$
81 $[81, 3, -3]$ $-2$
83 $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ $\phantom{-}0$
83 $[83, 83, 4w^{3} - 18w - 1]$ $\phantom{-}0$
89 $[89, 89, -2w^{3} + 10w + 1]$ $\phantom{-}12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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