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: | $[31,31,-2w^{2} + 3w + 11]$ |
| Dimension: | $26$ |
| CM: | no |
| Base change: | no |
| 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 | $[61, 61, 2w^{2} - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31,31,-2w^{2} + 3w + 11]$ | $-1$ |