# Properties

 Label 4.4.5725.1-31.1-c Base field 4.4.5725.1 Weight $[2, 2, 2, 2]$ Level norm $31$ Level $[31, 31, w^{3} - 6w + 1]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.5725.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} + 6x + 11$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[31, 31, w^{3} - 6w + 1]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 4x - 1$$
Norm Prime Eigenvalue
9 $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ $\phantom{-}e$
9 $[9, 3, -w + 1]$ $\phantom{-}e$
11 $[11, 11, w]$ $-\frac{1}{2}e + \frac{5}{2}$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $-\frac{1}{2}e - \frac{5}{2}$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $\phantom{-}2e + 5$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $-\frac{3}{2}e - \frac{9}{2}$
16 $[16, 2, 2]$ $-\frac{1}{2}e - \frac{15}{2}$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $-\frac{1}{2}e - \frac{3}{2}$
29 $[29, 29, -w - 3]$ $-\frac{1}{2}e + \frac{1}{2}$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $-2e - 5$
31 $[31, 31, w^{3} - 6w + 1]$ $\phantom{-}1$
31 $[31, 31, w^{3} - 6w - 2]$ $-2e - 7$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $-\frac{7}{2}e - \frac{19}{2}$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $\phantom{-}4e + 8$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $-\frac{1}{2}e - \frac{27}{2}$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $-2e - 4$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $-\frac{9}{2}e - \frac{31}{2}$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $\phantom{-}5e + 11$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $\phantom{-}\frac{7}{2}e + \frac{17}{2}$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $-\frac{3}{2}e + \frac{7}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, w^{3} - 6w + 1]$ $-1$