# Properties

 Base field 4.4.8768.1 Weight [2, 2, 2, 2] Level norm 31 Level $[31, 31, w^{2} - 5]$ Label 4.4.8768.1-31.1-a 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 $[31, 31, w^{2} - 5]$ Label 4.4.8768.1-31.1-a Dimension 4 Is CM no Is base change no Parent newspace dimension 23

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut 5x^{3}$$ $$\mathstrut +\mathstrut 3x^{2}$$ $$\mathstrut -\mathstrut 5x$$ $$\mathstrut +\mathstrut 1$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
7 $[7, 7, w]$ $-e^{3} - 6e^{2} - 7e + 2$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}2e^{3} + 10e^{2} + 7e - 7$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}e^{3} + 5e^{2} + 5e - 1$
7 $[7, 7, w - 1]$ $\phantom{-}2e^{3} + 11e^{2} + 11e - 7$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $-2e^{3} - 11e^{2} - 9e + 9$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $-4e^{3} - 22e^{2} - 24e + 13$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}1$
31 $[31, 31, -w^{2} + 2w + 4]$ $-e^{3} - 6e^{2} - 5e + 4$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $-8e^{3} - 40e^{2} - 32e + 20$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}2e^{3} + 12e^{2} + 13e - 14$
47 $[47, 47, w^{2} - 2w - 5]$ $-2e^{3} - 8e^{2} - 4e - 3$
47 $[47, 47, w^{2} - 6]$ $-5e^{3} - 25e^{2} - 19e + 16$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-3e^{3} - 16e^{2} - 20e + 1$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}3e^{3} + 14e^{2} + 8e - 8$
79 $[79, 79, -w - 3]$ $-2e^{3} - 12e^{2} - 14e + 5$
79 $[79, 79, w - 4]$ $\phantom{-}10e^{3} + 50e^{2} + 41e - 21$
81 $[81, 3, -3]$ $-6e^{3} - 31e^{2} - 22e + 16$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}12e^{3} + 62e^{2} + 56e - 34$
89 $[89, 89, w^{2} + w - 4]$ $-3e^{3} - 18e^{2} - 22e + 13$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, w^{2} - 5]$ $-1$