Base field \(\Q(\sqrt{86}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 86\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, 7w + 65]$ |
| Dimension: | $52$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $116$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{52} - 72x^{50} + 2419x^{48} - 50391x^{46} + 729447x^{44} - 7794270x^{42} + 63741113x^{40} - 408248807x^{38} + 2078458701x^{36} - 8489569503x^{34} + 27960930155x^{32} - 74379088094x^{30} + 159584913482x^{28} - 275011693872x^{26} + 377973613356x^{24} - 410128282154x^{22} + 346572615060x^{20} - 224008856073x^{18} + 108130197873x^{16} - 37721859587x^{14} + 9070539915x^{12} - 1397769463x^{10} + 122498636x^{8} - 5020646x^{6} + 84781x^{4} - 528x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w + 102]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 9]$ | $...$ |
| 5 | $[5, 5, w + 9]$ | $...$ |
| 7 | $[7, 7, 4w - 37]$ | $...$ |
| 7 | $[7, 7, 4w + 37]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, 7w + 65]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -7w + 65]$ | $...$ |
| 17 | $[17, 17, -2w - 19]$ | $...$ |
| 17 | $[17, 17, 2w - 19]$ | $...$ |
| 29 | $[29, 29, -15w + 139]$ | $...$ |
| 29 | $[29, 29, -15w - 139]$ | $...$ |
| 37 | $[37, 37, -w - 7]$ | $...$ |
| 37 | $[37, 37, w - 7]$ | $...$ |
| 41 | $[41, 41, -40w + 371]$ | $...$ |
| 41 | $[41, 41, 62w - 575]$ | $...$ |
| 43 | $[43, 43, -51w + 473]$ | $...$ |
| 59 | $[59, 59, -5w + 47]$ | $...$ |
| 59 | $[59, 59, 5w + 47]$ | $...$ |
| 61 | $[61, 61, -w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, 7w + 65]$ | $-1$ |