Base field \(\Q(\sqrt{123}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 123\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $24$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $64$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{24} - 126x^{22} + 6515x^{20} - 178684x^{18} + 2814087x^{16} - 25948674x^{14} + 139496645x^{12} - 434112676x^{10} + 768373380x^{8} - 744514416x^{6} + 359881056x^{4} - 69704064x^{2} + 3779136\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 11]$ | $...$ |
| 3 | $[3, 3, w]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, w + 15]$ | $...$ |
| 19 | $[19, 19, w + 3]$ | $...$ |
| 19 | $[19, 19, w + 16]$ | $...$ |
| 23 | $[23, 23, -w - 10]$ | $...$ |
| 23 | $[23, 23, w - 10]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 29 | $[29, 29, w + 6]$ | $...$ |
| 29 | $[29, 29, w + 23]$ | $...$ |
| 37 | $[37, 37, 9w + 100]$ | $...$ |
| 37 | $[37, 37, -2w - 23]$ | $...$ |
| 41 | $[41, 41, w]$ | $...$ |
| 53 | $[53, 53, w + 21]$ | $...$ |
| 53 | $[53, 53, w + 32]$ | $...$ |
| 59 | $[59, 59, -w - 8]$ | $...$ |
| 59 | $[59, 59, w - 8]$ | $...$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).