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: | $[7,7,-w + 2]$ |
| Dimension: | $62$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $244$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{62} - 86x^{60} + 3505x^{58} - 90088x^{56} + 1639410x^{54} - 22480846x^{52} + 241397145x^{50} - 2082384829x^{48} + 14690782008x^{46} - 85844830818x^{44} + 419317116742x^{42} - 1723248864666x^{40} + 5984737611891x^{38} - 17612015789575x^{36} + 43972423309373x^{34} - 93138496917930x^{32} + 167143028574025x^{30} - 253489287225535x^{28} + 323665356043755x^{26} - 346143314774316x^{24} + 307979586387795x^{22} - 226036122282536x^{20} + 135368840965174x^{18} - 65247573089528x^{16} + 24866762162848x^{14} - 7321094156863x^{12} + 1613475341580x^{10} - 254619490000x^{8} + 26914693239x^{6} - 1704759845x^{4} + 51427815x^{2} - 320529\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 11]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $-1$ |
| 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
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-w + 2]$ | $1$ |