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: | $[7, 7, 4w - 37]$ |
| Dimension: | $31$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $62$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{31} + 6x^{30} - 22x^{29} - 192x^{28} + 120x^{27} + 2694x^{26} + 1159x^{25} - 21764x^{24} - 21981x^{23} + 111632x^{22} + 159780x^{21} - 377072x^{20} - 689573x^{19} + 836262x^{18} + 1947789x^{17} - 1150698x^{16} - 3711896x^{15} + 772624x^{14} + 4775638x^{13} + 221848x^{12} - 4054995x^{11} - 922436x^{10} + 2152240x^{9} + 793826x^{8} - 632769x^{7} - 320202x^{6} + 71576x^{5} + 55308x^{4} + 3196x^{3} - 1840x^{2} - 252x - 8\) |
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 | $[7, 7, 4w - 37]$ | $\phantom{-}1$ |
| 7 | $[7, 7, 4w + 37]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, 7w + 65]$ | $...$ |
| 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 |
|---|---|---|
| $7$ | $[7, 7, 4w - 37]$ | $-1$ |