Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[10,10,-w + 3]$ |
Dimension: | $16$ |
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:
\(x^{16} + 4x^{15} - 17x^{14} - 78x^{13} + 102x^{12} + 580x^{11} - 265x^{10} - 2102x^{9} + 308x^{8} + 3905x^{7} - 212x^{6} - 3522x^{5} + 162x^{4} + 1335x^{3} - 34x^{2} - 150x - 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $-1$ |
5 | $[5, 5, -4w + 37]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 2]$ | $...$ |
7 | $[7, 7, w + 4]$ | $...$ |
9 | $[9, 3, 3]$ | $...$ |
17 | $[17, 17, w + 6]$ | $...$ |
17 | $[17, 17, w + 10]$ | $...$ |
19 | $[19, 19, -2w + 19]$ | $...$ |
19 | $[19, 19, -2w - 17]$ | $...$ |
23 | $[23, 23, w + 5]$ | $...$ |
23 | $[23, 23, w + 17]$ | $...$ |
37 | $[37, 37, w + 1]$ | $...$ |
37 | $[37, 37, w + 35]$ | $...$ |
41 | $[41, 41, -22w + 203]$ | $...$ |
41 | $[41, 41, -6w + 55]$ | $...$ |
43 | $[43, 43, w + 20]$ | $...$ |
43 | $[43, 43, w + 22]$ | $...$ |
53 | $[53, 53, w + 13]$ | $...$ |
53 | $[53, 53, w + 39]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w + 1]$ | $1$ |
$5$ | $[5,5,4w + 33]$ | $-1$ |