# 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-c Dimension 13 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-c Dimension 13 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:
$$x^{13}$$ $$\mathstrut -\mathstrut x^{12}$$ $$\mathstrut -\mathstrut 29x^{11}$$ $$\mathstrut +\mathstrut 25x^{10}$$ $$\mathstrut +\mathstrut 278x^{9}$$ $$\mathstrut -\mathstrut 165x^{8}$$ $$\mathstrut -\mathstrut 1084x^{7}$$ $$\mathstrut +\mathstrut 389x^{6}$$ $$\mathstrut +\mathstrut 1612x^{5}$$ $$\mathstrut -\mathstrut 566x^{4}$$ $$\mathstrut -\mathstrut 948x^{3}$$ $$\mathstrut +\mathstrut 359x^{2}$$ $$\mathstrut +\mathstrut 190x$$ $$\mathstrut -\mathstrut 77$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
7 $[7, 7, w]$ $...$
7 $[7, 7, -w^{2} + 2w + 1]$ $...$
7 $[7, 7, w^{2} - 2]$ $...$
7 $[7, 7, w - 1]$ $...$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $...$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $...$
31 $[31, 31, w^{2} - 5]$ $-1$
31 $[31, 31, -w^{2} + 2w + 4]$ $...$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $...$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $...$
47 $[47, 47, w^{2} - 2w - 5]$ $...$
47 $[47, 47, w^{2} - 6]$ $...$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $...$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $...$
79 $[79, 79, -w - 3]$ $...$
79 $[79, 79, w - 4]$ $...$
81 $[81, 3, -3]$ $...$
89 $[89, 89, w^{2} - 3w - 2]$ $...$
89 $[89, 89, w^{2} + w - 4]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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