# Properties

 Label 4.4.4525.1-31.1-b Base field 4.4.4525.1 Weight $[2, 2, 2, 2]$ Level norm $31$ Level $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.4525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 3x + 9$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $7$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 4x^{3} - 5x^{2} + 25x - 18$$
Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $\phantom{-}3e^{3} - 8e^{2} - 26e + 42$
9 $[9, 3, -w]$ $\phantom{-}2e^{3} - 5e^{2} - 18e + 26$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}2e^{3} - 5e^{2} - 18e + 26$
16 $[16, 2, 2]$ $-e - 1$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $\phantom{-}e^{3} - 2e^{2} - 9e + 10$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $-2e^{3} + 5e^{2} + 19e - 26$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $-1$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $-3e^{3} + 7e^{2} + 26e - 32$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $-7e^{3} + 19e^{2} + 61e - 96$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $\phantom{-}6e^{3} - 15e^{2} - 52e + 78$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $-6e^{3} + 16e^{2} + 49e - 80$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $\phantom{-}e^{3} - 2e^{2} - 10e + 10$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $-e^{3} + e^{2} + 10e$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-e^{3} + 3e^{2} + 8e - 12$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}12e^{3} - 33e^{2} - 103e + 168$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $\phantom{-}2e^{3} - 6e^{2} - 18e + 30$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $\phantom{-}2e^{3} - 4e^{2} - 18e + 18$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}13e^{3} - 35e^{2} - 110e + 174$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $-4e^{3} + 10e^{2} + 37e - 48$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $1$