# Properties

 Label 4.4.13824.1-16.1-i Base field 4.4.13824.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $6$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.13824.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} + 6$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $6$ CM: no Base change: yes Newspace dimension: $15$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 24x^{4} + 176x^{2} - 368$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}0$
3 $[3, 3, w^{2} - w - 3]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + w + 1]$ $-\frac{1}{2}e^{3} + 5e$
11 $[11, 11, -w^{2} - w + 1]$ $-\frac{1}{2}e^{3} + 5e$
13 $[13, 13, w^{3} - 4w + 1]$ $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 20$
13 $[13, 13, -w^{3} + 4w + 1]$ $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 20$
25 $[25, 5, -w^{2} - 2w + 1]$ $-\frac{1}{2}e^{4} + 8e^{2} - 26$
25 $[25, 5, w^{2} - 2w - 1]$ $-\frac{1}{2}e^{4} + 8e^{2} - 26$
37 $[37, 37, w^{3} - 3w - 1]$ $-e^{4} + 15e^{2} - 46$
37 $[37, 37, w^{3} - 3w + 1]$ $-e^{4} + 15e^{2} - 46$
59 $[59, 59, w^{2} - w - 5]$ $-\frac{1}{2}e^{5} + 7e^{3} - 19e$
59 $[59, 59, -w^{2} - w + 5]$ $-\frac{1}{2}e^{5} + 7e^{3} - 19e$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $\phantom{-}e^{4} - 15e^{2} + 46$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $\phantom{-}e^{4} - 15e^{2} + 46$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}3e^{2} - 22$
73 $[73, 73, 2w - 1]$ $-e^{4} + 13e^{2} - 26$
73 $[73, 73, -2w - 1]$ $-e^{4} + 13e^{2} - 26$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}3e^{2} - 22$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{15}{2}e^{3} + 21e$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{15}{2}e^{3} + 21e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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