# Properties

 Base field 4.4.11525.1 Weight [2, 2, 2, 2] Level norm 31 Level $[31,31,\frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ Label 4.4.11525.1-31.2-a Dimension 15 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.11525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 5x + 25$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[31,31,\frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ Label 4.4.11525.1-31.2-a Dimension 15 Is CM no Is base change no Parent newspace dimension 33

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{15}$$ $$\mathstrut +\mathstrut 3x^{14}$$ $$\mathstrut -\mathstrut 46x^{13}$$ $$\mathstrut -\mathstrut 153x^{12}$$ $$\mathstrut +\mathstrut 788x^{11}$$ $$\mathstrut +\mathstrut 2986x^{10}$$ $$\mathstrut -\mathstrut 6064x^{9}$$ $$\mathstrut -\mathstrut 28280x^{8}$$ $$\mathstrut +\mathstrut 18645x^{7}$$ $$\mathstrut +\mathstrut 136921x^{6}$$ $$\mathstrut +\mathstrut 1371x^{5}$$ $$\mathstrut -\mathstrut 330358x^{4}$$ $$\mathstrut -\mathstrut 102262x^{3}$$ $$\mathstrut +\mathstrut 354759x^{2}$$ $$\mathstrut +\mathstrut 112194x$$ $$\mathstrut -\mathstrut 135162$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $...$
11 $[11, 11, w + 1]$ $...$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $...$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $...$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $...$
19 $[19, 19, w - 1]$ $...$
29 $[29, 29, w^{2} - w - 8]$ $...$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $...$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $...$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}1$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $...$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $...$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $...$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $...$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $...$
71 $[71, 71, w^{2} - 8]$ $...$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31,31,\frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $-1$