# Properties

 Label 4.4.12725.1-16.1-d Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $12$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $12$ CM: no Base change: yes Newspace dimension: $19$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{12} - 7x^{11} - 45x^{10} + 350x^{9} + 392x^{8} - 4679x^{7} + 1153x^{6} + 20492x^{5} - 13640x^{4} - 28280x^{3} + 20368x^{2} + 6776x - 3632$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $...$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}e$
11 $[11, 11, w - 2]$ $...$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, w^{2} - 2w - 5]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
25 $[25, 5, -2w^{2} + 2w + 11]$ $...$
29 $[29, 29, w]$ $...$
29 $[29, 29, 2w^{2} - w - 10]$ $...$
29 $[29, 29, -2w^{2} + 3w + 9]$ $...$
29 $[29, 29, w - 1]$ $...$
31 $[31, 31, w^{3} - 6w - 6]$ $...$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $...$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $...$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $...$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $...$
59 $[59, 59, 2w^{2} - w - 13]$ $...$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $...$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$