# Properties

 Label 4.4.9792.1-16.1-a Base field 4.4.9792.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.9792.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 4x^{3} - 20x^{2} - 48x - 16$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ $\phantom{-}0$
7 $[7, 7, w]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{10}{3}e - \frac{14}{3}$
7 $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ $-\frac{1}{6}e^{3} - \frac{1}{2}e^{2} + \frac{10}{3}e + \frac{8}{3}$
9 $[9, 3, w^{3} - 4w^{2} - w + 9]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{13}{3}e - \frac{14}{3}$
17 $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $-\frac{1}{6}e^{3} - \frac{1}{2}e^{2} + \frac{13}{3}e + \frac{14}{3}$
17 $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ $-\frac{1}{2}e^{2} - e + 6$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{1}{2}e^{2} + e - 6$
23 $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ $-\frac{1}{3}e^{3} - e^{2} + \frac{26}{3}e + \frac{28}{3}$
23 $[23, 23, -w^{2} + 2w + 3]$ $-\frac{1}{3}e^{3} - e^{2} + \frac{26}{3}e + \frac{28}{3}$
31 $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{10}{3}e - \frac{14}{3}$
31 $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ $-\frac{1}{6}e^{3} - \frac{1}{2}e^{2} + \frac{10}{3}e + \frac{8}{3}$
41 $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 13e - 14$
41 $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 13e - 14$
49 $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ $-8$
71 $[71, 71, w^{2} - 2w - 2]$ $-\frac{1}{6}e^{3} - e^{2} + \frac{10}{3}e + \frac{32}{3}$
71 $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ $-\frac{1}{6}e^{3} + \frac{16}{3}e - \frac{4}{3}$
73 $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ $\phantom{-}\frac{2}{3}e^{3} + 2e^{2} - \frac{40}{3}e - \frac{68}{3}$
73 $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ $-\frac{2}{3}e^{3} - 2e^{2} + \frac{40}{3}e + \frac{20}{3}$
79 $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{10}{3}e - \frac{56}{3}$
79 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $-\frac{1}{6}e^{3} - \frac{1}{2}e^{2} + \frac{10}{3}e - \frac{34}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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