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: | $62$ |
| 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:
| \(x^{62} - 91x^{60} + 3921x^{58} - 106424x^{56} + 2042121x^{54} - 29473176x^{52} + 332343392x^{50} - 3002437888x^{48} + 22110734664x^{46} - 134351425771x^{44} + 679306446781x^{42} - 2874412479221x^{40} + 10214474145020x^{38} - 30534816106494x^{36} + 76792652716140x^{34} - 162249956158567x^{32} + 287196055974178x^{30} - 424121992620211x^{28} + 519639532688660x^{26} - 524514653137468x^{24} + 432433938122834x^{22} - 288198482003393x^{20} + 153350098057669x^{18} - 64176789367876x^{16} + 20734779300081x^{14} - 5049712093783x^{12} + 897539314176x^{10} - 111149151367x^{8} + 8923167273x^{6} - 410230661x^{4} + 8488241x^{2} - 55225\) |
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 | $[11, 11, 7w + 65]$ | $-1$ |
| 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 |
|---|---|---|
| $11$ | $[11, 11, 7w + 65]$ | $1$ |