# Properties

 Label 4.4.8768.1-28.2-e Base field 4.4.8768.1 Weight $[2, 2, 2, 2]$ Level norm $28$ Level $[28, 14, -w^{3} + 3w^{2} + w - 4]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8768.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 6x + 7$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[28, 14, -w^{3} + 3w^{2} + w - 4]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 23x^{2} - 12x + 37$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}1$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}1$
7 $[7, 7, w^{2} - 2]$ $-\frac{1}{6}e^{3} + \frac{1}{6}e^{2} + \frac{19}{6}e + \frac{1}{3}$
7 $[7, 7, w - 1]$ $-\frac{1}{6}e^{3} + \frac{1}{6}e^{2} + \frac{19}{6}e + \frac{1}{3}$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + \frac{9}{2}$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{3}e^{2} - \frac{11}{3}e - \frac{35}{6}$
31 $[31, 31, w^{2} - 5]$ $-\frac{1}{6}e^{3} + \frac{1}{6}e^{2} + \frac{25}{6}e - \frac{8}{3}$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{6}e^{2} - \frac{19}{6}e + \frac{5}{3}$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}4$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} + \frac{16}{3}e - \frac{10}{3}$
47 $[47, 47, w^{2} - 2w - 5]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{3}e^{2} - \frac{17}{3}e - \frac{23}{6}$
47 $[47, 47, w^{2} - 6]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{6}e^{2} - \frac{35}{6}e - \frac{7}{6}$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} + \frac{13}{3}e - \frac{10}{3}$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} + \frac{25}{3}e + \frac{8}{3}$
79 $[79, 79, -w - 3]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{2}{3}e^{2} - \frac{14}{3}e + \frac{49}{6}$
79 $[79, 79, w - 4]$ $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} + \frac{22}{3}e - \frac{1}{3}$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - \frac{25}{2}$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{6}e^{2} - \frac{35}{6}e + \frac{17}{6}$
89 $[89, 89, w^{2} + w - 4]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{28}{3}e - \frac{11}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + w + 3]$ $-1$
$7$ $[7, 7, -w^{2} + 2w + 1]$ $-1$