Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 31
Level $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$
Label 4.4.11525.1-31.1-a
Dimension 15
CM no
Base change no

Related objects

Downloads

Learn more about

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 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$
Label 4.4.11525.1-31.1-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:
\(x^{15} \) \(\mathstrut +\mathstrut 3x^{14} \) \(\mathstrut -\mathstrut 46x^{13} \) \(\mathstrut -\mathstrut 153x^{12} \) \(\mathstrut +\mathstrut 788x^{11} \) \(\mathstrut +\mathstrut 2986x^{10} \) \(\mathstrut -\mathstrut 6064x^{9} \) \(\mathstrut -\mathstrut 28280x^{8} \) \(\mathstrut +\mathstrut 18645x^{7} \) \(\mathstrut +\mathstrut 136921x^{6} \) \(\mathstrut +\mathstrut 1371x^{5} \) \(\mathstrut -\mathstrut 330358x^{4} \) \(\mathstrut -\mathstrut 102262x^{3} \) \(\mathstrut +\mathstrut 354759x^{2} \) \(\mathstrut +\mathstrut 112194x \) \(\mathstrut -\mathstrut 135162\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $...$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}e$
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 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $\phantom{-}1$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $...$
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 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-1$