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: | $[10, 10, 3w - 28]$ |
Dimension: | $16$ |
CM: | no |
Base change: | no |
Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} - 53x^{14} - 7x^{13} + 1088x^{12} + 240x^{11} - 11161x^{10} - 2572x^{9} + 61898x^{8} + 9997x^{7} - 185824x^{6} - 4660x^{5} + 277360x^{4} - 43720x^{3} - 151305x^{2} + 53514x - 4212\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -11w + 102]$ | $-1$ |
5 | $[5, 5, w - 9]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 9]$ | $-1$ |
7 | $[7, 7, 4w - 37]$ | $...$ |
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 |
---|---|---|
$2$ | $[2, 2, -11w + 102]$ | $1$ |
$5$ | $[5, 5, w + 9]$ | $1$ |