# Properties

 Label 4.4.9248.1-16.3-f Base field 4.4.9248.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, -w^{2} + 3]$ Dimension $4$ CM no Base change yes

# Related objects

• L-function not available

## 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: $[16, 4, -w^{2} + 3]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} - 9x^{2} + 12$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}2e$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}2e$
19 $[19, 19, -w^{3} + 3w + 1]$ $-e^{3} + 5e$
19 $[19, 19, -w^{3} + 3w - 1]$ $-e^{3} + 5e$
43 $[43, 43, -w^{2} + w - 1]$ $\phantom{-}2e^{2} - 14$
43 $[43, 43, w^{2} + w + 1]$ $\phantom{-}2e^{2} - 14$
49 $[49, 7, w^{3} + w^{2} - 6w - 3]$ $-2e^{3} + 12e$
49 $[49, 7, w^{3} - w^{2} - 6w + 3]$ $-2e^{3} + 12e$
53 $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ $-4e^{2} + 18$
53 $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ $-4e^{2} + 18$
59 $[59, 59, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2e^{2} - 6$
59 $[59, 59, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}2e^{2} - 6$
67 $[67, 67, 3w^{3} - 13w + 1]$ $\phantom{-}e^{3} - 5e$
67 $[67, 67, -w^{3} + w^{2} + 6w - 5]$ $\phantom{-}e^{3} - 5e$
81 $[81, 3, -3]$ $-4e^{2} + 22$
83 $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ $-2e^{2} + 6$
83 $[83, 83, 4w^{3} - 18w - 1]$ $-2e^{2} + 6$
89 $[89, 89, -2w^{3} + 10w + 1]$ $\phantom{-}2e^{3} - 16e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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