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

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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:
\(x^{13} \) \(\mathstrut -\mathstrut x^{12} \) \(\mathstrut -\mathstrut 29x^{11} \) \(\mathstrut +\mathstrut 25x^{10} \) \(\mathstrut +\mathstrut 278x^{9} \) \(\mathstrut -\mathstrut 165x^{8} \) \(\mathstrut -\mathstrut 1084x^{7} \) \(\mathstrut +\mathstrut 389x^{6} \) \(\mathstrut +\mathstrut 1612x^{5} \) \(\mathstrut -\mathstrut 566x^{4} \) \(\mathstrut -\mathstrut 948x^{3} \) \(\mathstrut +\mathstrut 359x^{2} \) \(\mathstrut +\mathstrut 190x \) \(\mathstrut -\mathstrut 77\)

  Show full eigenvalues   Hide large eigenvalues

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