Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[10,10,-w - 6]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 9x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, 23w - 156]$ | $-1$ |
3 | $[3, 3, -w - 7]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - \frac{8}{3}$ |
3 | $[3, 3, w - 7]$ | $\phantom{-}e$ |
5 | $[5, 5, -9w + 61]$ | $\phantom{-}1$ |
5 | $[5, 5, -9w - 61]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - \frac{8}{3}$ |
7 | $[7, 7, 4w - 27]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - \frac{5}{3}$ |
7 | $[7, 7, 4w + 27]$ | $-e - 1$ |
23 | $[23, 23, 78w - 529]$ | $-\frac{1}{3}e^{2} - \frac{1}{3}e - \frac{7}{3}$ |
37 | $[37, 37, -w - 3]$ | $\phantom{-}e - 6$ |
37 | $[37, 37, w - 3]$ | $-\frac{4}{3}e^{2} + \frac{2}{3}e + \frac{23}{3}$ |
41 | $[41, 41, -2w + 15]$ | $-\frac{2}{3}e^{2} - \frac{5}{3}e + \frac{16}{3}$ |
41 | $[41, 41, 2w + 15]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{2}{3}e - \frac{13}{3}$ |
53 | $[53, 53, -3w - 19]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{4}{3}e - \frac{43}{3}$ |
53 | $[53, 53, 3w - 19]$ | $-e^{2} + 2e + 11$ |
59 | $[59, 59, 11w - 75]$ | $-\frac{5}{3}e^{2} - \frac{2}{3}e + \frac{25}{3}$ |
59 | $[59, 59, -11w - 75]$ | $-e^{2} + 1$ |
61 | $[61, 61, -5w + 33]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{4}{3}e - \frac{20}{3}$ |
61 | $[61, 61, 5w + 33]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{1}{3}e - \frac{7}{3}$ |
73 | $[73, 73, -24w - 163]$ | $-e^{2} + e + 14$ |
73 | $[73, 73, -24w + 163]$ | $-\frac{2}{3}e^{2} - \frac{2}{3}e - \frac{8}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-23w - 156]$ | $1$ |
$5$ | $[5,5,9w - 61]$ | $-1$ |