# Properties

 Base field 4.4.8789.1 Weight [2, 2, 2, 2] Level norm 31 Level $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ Label 4.4.8789.1-31.1-g Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

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

## Form

 Weight [2, 2, 2, 2] Level $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ Label 4.4.8789.1-31.1-g Dimension 4 Is CM no Is base change no Parent newspace dimension 21

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - x^{3} - 15x^{2} + 20x + 4$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{1}{3}e^{3} - 4e + \frac{2}{3}$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}\frac{1}{3}e^{3} - 4e + \frac{8}{3}$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-2$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{3}e^{3} - 5e + \frac{11}{3}$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}2$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{3}{2}e - \frac{11}{3}$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - 6e + \frac{14}{3}$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}\frac{1}{3}e^{3} - 5e + \frac{2}{3}$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}\frac{1}{3}e^{3} - 5e + \frac{20}{3}$
29 $[29, 29, w^{2} - w - 3]$ $-e + 2$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-1$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-\frac{1}{3}e^{3} + 4e - \frac{20}{3}$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}e^{2} - 4$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $-e^{2} - e + 12$
61 $[61, 61, -w - 3]$ $-\frac{1}{3}e^{3} + 2e - \frac{2}{3}$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-\frac{1}{6}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e + \frac{17}{3}$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{43}{3}$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{5}{2}e - \frac{5}{3}$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{3}{2}e^{2} - \frac{9}{2}e + \frac{49}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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