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: | $[5, 5, w + 1]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + 5x^{10} - 11x^{9} - 79x^{8} + 5x^{7} + 396x^{6} + 264x^{5} - 599x^{4} - 724x^{3} - 128x^{2} + 60x - 1\) |
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 | $[5, 5, w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $-\frac{31687}{3881}e^{10} - \frac{130218}{3881}e^{9} + \frac{464412}{3881}e^{8} + \frac{2089718}{3881}e^{7} - \frac{2018216}{3881}e^{6} - \frac{10753943}{3881}e^{5} + \frac{1208644}{3881}e^{4} + \frac{17939274}{3881}e^{3} + \frac{6977951}{3881}e^{2} - \frac{2247157}{3881}e + \frac{28698}{3881}$ |
| 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 | $[37, 37, w - 5]$ | $\phantom{-}\frac{7712}{3881}e^{10} + \frac{31445}{3881}e^{9} - \frac{114109}{3881}e^{8} - \frac{505232}{3881}e^{7} + \frac{507620}{3881}e^{6} + \frac{2604910}{3881}e^{5} - \frac{369750}{3881}e^{4} - \frac{4367931}{3881}e^{3} - \frac{1603206}{3881}e^{2} + \frac{607788}{3881}e + \frac{11119}{3881}$ |
| 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 |
|---|---|---|
| $5$ | $[5, 5, w + 1]$ | $-1$ |