Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 31
Level $[31,31,-2w^{2} + 3w + 11]$
Label 4.4.17725.1-31.2-a
Dimension 26
CM no
Base change no

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Base field 4.4.17725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[31,31,-2w^{2} + 3w + 11]$
Label 4.4.17725.1-31.2-a
Dimension 26
Is CM no
Is base change no
Parent newspace dimension 59

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{26} + 6x^{25} - 111x^{24} - 705x^{23} + 4943x^{22} + 34500x^{21} - 111967x^{20} - 917818x^{19} + 1322594x^{18} + 14602261x^{17} - 6574875x^{16} - 145273138x^{15} - 15838069x^{14} + 929439921x^{13} + 376572152x^{12} - 3904877675x^{11} - 2043812206x^{10} + 10890628687x^{9} + 5545912953x^{8} - 20030547927x^{7} - 7902440752x^{6} + 23382723058x^{5} + 4980506496x^{4} - 15663200706x^{3} - 38820006x^{2} + 4561190892x - 928621944\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $...$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $...$
19 $[19, 19, w + 1]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
19 $[19, 19, -w^{2} + 2w + 5]$ $...$
19 $[19, 19, -w + 2]$ $...$
25 $[25, 5, 2w^{2} - 2w - 13]$ $...$
29 $[29, 29, -w^{2} + 9]$ $...$
29 $[29, 29, -w^{2} + 2w + 6]$ $...$
29 $[29, 29, w^{2} - 7]$ $...$
29 $[29, 29, -w^{2} + 2w + 8]$ $...$
31 $[31, 31, -2w^{2} + w + 12]$ $...$
31 $[31, 31, 2w^{2} - 3w - 11]$ $\phantom{-}1$
41 $[41, 41, -w]$ $...$
41 $[41, 41, -w + 1]$ $...$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $...$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $...$
61 $[61, 61, 2w^{2} - 3w - 14]$ $...$
61 $[61, 61, 2w^{2} - w - 15]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31,31,-2w^{2} + 3w + 11]$ $-1$