Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[12, 6, 2w]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} + 38x^{16} + 595x^{14} + 4968x^{12} + 23891x^{10} + 66518x^{8} + 101873x^{6} + 76113x^{4} + 23392x^{2} + 2304\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w + 8]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $...$ |
| 13 | $[13, 13, w + 9]$ | $...$ |
| 17 | $[17, 17, w]$ | $...$ |
| 17 | $[17, 17, w + 16]$ | $...$ |
| 31 | $[31, 31, -w - 4]$ | $...$ |
| 31 | $[31, 31, w - 5]$ | $...$ |
| 41 | $[41, 41, 3w - 22]$ | $...$ |
| 47 | $[47, 47, w + 19]$ | $...$ |
| 47 | $[47, 47, w + 27]$ | $...$ |
| 53 | $[53, 53, w + 14]$ | $...$ |
| 53 | $[53, 53, w + 38]$ | $...$ |
| 59 | $[59, 59, -w - 10]$ | $...$ |
| 59 | $[59, 59, w - 11]$ | $...$ |
| 61 | $[61, 61, 2w - 13]$ | $-\frac{661838}{41983479}e^{16} - \frac{22809764}{41983479}e^{14} - \frac{34954530}{4664831}e^{12} - \frac{247051103}{4664831}e^{10} - \frac{8571877630}{41983479}e^{8} - \frac{1975855612}{4664831}e^{6} - \frac{18703396540}{41983479}e^{4} - \frac{9527595626}{41983479}e^{2} - \frac{162974614}{4664831}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $\frac{265417}{3582590208}e^{17} + \frac{6596563}{1791295104}e^{15} + \frac{253283083}{3582590208}e^{13} + \frac{101253665}{149274592}e^{11} + \frac{12368848811}{3582590208}e^{9} + \frac{15948054331}{1791295104}e^{7} + \frac{32975340569}{3582590208}e^{5} - \frac{439628253}{1194196736}e^{3} - \frac{592935629}{223911888}e$ |
| $4$ | $[4, 2, 2]$ | $-1$ |