# Properties

 Label 4.4.19796.1-16.1-e Base field 4.4.19796.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19796.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + x + 8$$; narrow class number $$2$$ and class number $$1$$.

## Form

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

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 20x^{4} + 56x^{2} - 32$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}1$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $\phantom{-}0$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $-\frac{1}{4}e^{5} + \frac{9}{2}e^{3} - 5e$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 7e$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $-\frac{1}{8}e^{5} + 2e^{3}$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{2}e^{4} - 9e^{2} + 12$
31 $[31, 31, -w^{2} + w + 1]$ $-\frac{1}{2}e^{5} + \frac{19}{2}e^{3} - 18e$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - 6e$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $-\frac{3}{8}e^{5} + 7e^{3} - 11e$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $\phantom{-}\frac{1}{2}e^{4} - 8e^{2} + 6$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{2}e^{4} - 8e^{2} + 6$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $\phantom{-}\frac{1}{4}e^{5} - 5e^{3} + 13e$
61 $[61, 61, 2w^{2} - 7]$ $-\frac{1}{2}e^{5} + \frac{19}{2}e^{3} - 21e$
71 $[71, 71, w^{2} - 3w - 5]$ $-e^{4} + 19e^{2} - 28$
73 $[73, 73, 2w - 3]$ $\phantom{-}\frac{3}{8}e^{5} - \frac{15}{2}e^{3} + 19e$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 3e$
79 $[79, 79, 2w^{2} - 5]$ $-\frac{1}{2}e^{4} + 9e^{2} - 4$
81 $[81, 3, -3]$ $-e^{2} + 6$
101 $[101, 101, 2w^{2} - 4w - 9]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{19}{2}e^{3} + 19e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w^{2} + 2]$ $-1$
$2$ $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $-1$