Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, w + 3]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $99$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 17x^{14} + 10x^{13} + 205x^{12} + 129x^{11} + 1255x^{10} + 1016x^{9} + 5589x^{8} + 3726x^{7} + 9816x^{6} + 5704x^{5} + 12105x^{4} + 5588x^{3} + 3996x^{2} - 240x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, w + 1]$ | $...$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, w + 14]$ | $...$ |
| 19 | $[19, 19, w]$ | $...$ |
| 19 | $[19, 19, w + 18]$ | $...$ |
| 37 | $[37, 37, -w - 4]$ | $...$ |
| 37 | $[37, 37, w - 5]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, -w - 10]$ | $...$ |
| 53 | $[53, 53, w - 11]$ | $...$ |
| 61 | $[61, 61, w + 15]$ | $...$ |
| 61 | $[61, 61, w + 45]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $\frac{534894411171248255}{138295751747216132444}e^{15} + \frac{82941625557193091}{414887255241648397332}e^{14} + \frac{9069410185704986475}{138295751747216132444}e^{13} + \frac{17447764822113654133}{414887255241648397332}e^{12} + \frac{328605034255860549919}{414887255241648397332}e^{11} + \frac{55801637237540828951}{103721813810412099333}e^{10} + \frac{1005155745303612646091}{207443627620824198666}e^{9} + \frac{574893984694981333303}{138295751747216132444}e^{8} + \frac{2989379038370747410707}{138295751747216132444}e^{7} + \frac{6374261066808890698117}{414887255241648397332}e^{6} + \frac{2614886122566809153423}{69147875873608066222}e^{5} + \frac{811699302218013335123}{34573937936804033111}e^{4} + \frac{6447143229120615081183}{138295751747216132444}e^{3} + \frac{3292223504926907438597}{138295751747216132444}e^{2} + \frac{1557679533835325152963}{103721813810412099333}e + \frac{3398847527539748115}{34573937936804033111}$ |