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: | $[3,3,-w + 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} + 3x^{13} + 20x^{12} + 51x^{11} + 254x^{10} + 580x^{9} + 1571x^{8} + 2141x^{7} + 3899x^{6} + 4095x^{5} + 6462x^{4} + 4354x^{3} + 2604x^{2} + 392x + 49\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 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 |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $-\frac{57463151712704}{18580847037014549}e^{13} - \frac{329940423221169}{37161694074029098}e^{12} - \frac{2267213063705377}{37161694074029098}e^{11} - \frac{5604077071498749}{37161694074029098}e^{10} - \frac{2049925008524500}{2654406719573507}e^{9} - \frac{63543686338458539}{37161694074029098}e^{8} - \frac{87621667763474479}{18580847037014549}e^{7} - \frac{115025971620877732}{18580847037014549}e^{6} - \frac{436286977162939755}{37161694074029098}e^{5} - \frac{62406175242339603}{5308813439147014}e^{4} - \frac{362105392051378503}{18580847037014549}e^{3} - \frac{432318868008653613}{37161694074029098}e^{2} - \frac{21451631341948629}{2654406719573507}e - \frac{6467542780550369}{5308813439147014}$ |