Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 12 x^2 + 13 x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[31,31,-2 w^2 + 3 w + 11]$ |
| 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:
| \(x^{26} + 6 x^{25} - 111 x^{24} - 705 x^{23} + 4943 x^{22} + 34500 x^{21} - 111967 x^{20} - 917818 x^{19} + 1322594 x^{18} + 14602261 x^{17} - 6574875 x^{16} - 145273138 x^{15} - 15838069 x^{14} + 929439921 x^{13} + 376572152 x^{12} - 3904877675 x^{11} - 2043812206 x^{10} + 10890628687 x^9 + 5545912953 x^8 - 20030547927 x^7 - 7902440752 x^6 + 23382723058 x^5 + 4980506496 x^4 - 15663200706 x^3 - 38820006 x^2 + 4561190892 x - 928621944\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ | $...$ |
| 9 | $[9, 3, -w^3 + 8 w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, -w^2 + 6]$ | $...$ |
| 19 | $[19, 19, -w^2 + 2 w + 5]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 25 | $[25, 5, 2 w^2 - 2 w - 13]$ | $...$ |
| 29 | $[29, 29, -w^2 + 9]$ | $...$ |
| 29 | $[29, 29, -w^2 + 2 w + 6]$ | $...$ |
| 29 | $[29, 29, w^2 - 7]$ | $...$ |
| 29 | $[29, 29, -w^2 + 2 w + 8]$ | $...$ |
| 31 | $[31, 31, -2 w^2 + w + 12]$ | $...$ |
| 31 | $[31, 31, 2 w^2 - 3 w - 11]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w]$ | $...$ |
| 41 | $[41, 41, -w + 1]$ | $...$ |
| 49 | $[49, 7, w^3 + 2 w^2 - 10 w - 20]$ | $...$ |
| 49 | $[49, 7, w^3 - 5 w^2 - 3 w + 27]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - 3 w - 14]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31,31,-2 w^2 + 3 w + 11]$ | $-1$ |