Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, -w^{2} + 6]$ |
| Dimension: | $33$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $66$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{33} + 4x^{32} - 95x^{31} - 371x^{30} + 4007x^{29} + 15116x^{28} - 99476x^{27} - 357058x^{26} + 1625349x^{25} + 5436603x^{24} - 18516128x^{23} - 56145299x^{22} + 151852122x^{21} + 403124957x^{20} - 910672131x^{19} - 2030008685x^{18} + 4004373778x^{17} + 7144637376x^{16} - 12798002402x^{15} - 17316175778x^{14} + 29177179334x^{13} + 28105578608x^{12} - 46164020937x^{11} - 29103130271x^{10} + 48856549695x^{9} + 17467783673x^{8} - 32786054037x^{7} - 4644314753x^{6} + 12743205531x^{5} - 246794012x^{4} - 2377257916x^{3} + 284099876x^{2} + 116363351x - 7526940\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 11 | $[11, 11, w + 2]$ | $...$ |
| 13 | $[13, 13, w + 1]$ | $...$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $-1$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $...$ |
| 23 | $[23, 23, -w + 4]$ | $...$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $...$ |
| 31 | $[31, 31, w^{2} - 10]$ | $...$ |
| 41 | $[41, 41, w + 4]$ | $...$ |
| 41 | $[41, 41, w^{2} - 5]$ | $...$ |
| 41 | $[41, 41, -2w - 5]$ | $...$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $...$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $...$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $...$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{2} + 6]$ | $1$ |