# Properties

 Label 4.4.9792.1-4.1-a Base field 4.4.9792.1 Weight $[2, 2, 2, 2]$ Level norm $4$ Level $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ Dimension $4$ CM no Base change yes

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

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 58x^{2} + 800$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ $-1$
7 $[7, 7, w]$ $-\frac{1}{2}e^{2} + 13$
7 $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ $-\frac{1}{2}e^{2} + 13$
9 $[9, 3, w^{3} - 4w^{2} - w + 9]$ $\phantom{-}e$
17 $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $\phantom{-}\frac{3}{20}e^{3} - \frac{47}{10}e$
17 $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{40}e^{3} - \frac{29}{20}e$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{1}{40}e^{3} - \frac{29}{20}e$
23 $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ $\phantom{-}\frac{3}{40}e^{3} - \frac{27}{20}e$
23 $[23, 23, -w^{2} + 2w + 3]$ $\phantom{-}\frac{3}{40}e^{3} - \frac{27}{20}e$
31 $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $-e^{2} + 32$
31 $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ $-e^{2} + 32$
41 $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ $\phantom{-}\frac{1}{10}e^{3} - \frac{14}{5}e$
41 $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ $\phantom{-}\frac{1}{10}e^{3} - \frac{14}{5}e$
49 $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ $-e^{2} + 30$
71 $[71, 71, w^{2} - 2w - 2]$ $-\frac{2}{5}e^{3} + \frac{61}{5}e$
71 $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ $-\frac{2}{5}e^{3} + \frac{61}{5}e$
73 $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ $\phantom{-}e^{2} - 36$
73 $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ $\phantom{-}e^{2} - 36$
79 $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ $\phantom{-}0$
79 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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