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: | $[12, 6, -2w - 14]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 20x^{4} + 100x^{2} - 98\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, 23w - 156]$ | $\phantom{-}0$ |
3 | $[3, 3, -w - 7]$ | $\phantom{-}1$ |
3 | $[3, 3, w - 7]$ | $-\frac{1}{7}e^{4} + \frac{17}{7}e^{2} - 6$ |
5 | $[5, 5, -9w + 61]$ | $\phantom{-}e$ |
5 | $[5, 5, -9w - 61]$ | $-\frac{1}{7}e^{3} + \frac{10}{7}e$ |
7 | $[7, 7, 4w - 27]$ | $\phantom{-}e$ |
7 | $[7, 7, 4w + 27]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{16}{7}e^{3} + \frac{46}{7}e$ |
23 | $[23, 23, 78w - 529]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{16}{7}e^{3} + \frac{53}{7}e$ |
37 | $[37, 37, -w - 3]$ | $-\frac{1}{7}e^{5} + \frac{15}{7}e^{3} - \frac{43}{7}e$ |
37 | $[37, 37, w - 3]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{18}{7}e^{3} + \frac{59}{7}e$ |
41 | $[41, 41, -2w + 15]$ | $\phantom{-}\frac{3}{7}e^{4} - \frac{44}{7}e^{2} + 12$ |
41 | $[41, 41, 2w + 15]$ | $-\frac{2}{7}e^{4} + \frac{27}{7}e^{2} - 4$ |
53 | $[53, 53, -3w - 19]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{16}{7}e^{3} + \frac{39}{7}e$ |
53 | $[53, 53, 3w - 19]$ | $\phantom{-}\frac{1}{7}e^{5} - 3e^{3} + \frac{82}{7}e$ |
59 | $[59, 59, 11w - 75]$ | $-\frac{3}{7}e^{4} + \frac{44}{7}e^{2} - 20$ |
59 | $[59, 59, -11w - 75]$ | $-\frac{1}{7}e^{4} + \frac{24}{7}e^{2} - 14$ |
61 | $[61, 61, -5w + 33]$ | $-\frac{1}{7}e^{5} + \frac{13}{7}e^{3} - \frac{30}{7}e$ |
61 | $[61, 61, 5w + 33]$ | $-\frac{1}{7}e^{3} + \frac{10}{7}e$ |
73 | $[73, 73, -24w - 163]$ | $-\frac{3}{7}e^{4} + \frac{44}{7}e^{2} - 14$ |
73 | $[73, 73, -24w + 163]$ | $\phantom{-}\frac{3}{7}e^{4} - \frac{44}{7}e^{2} + 22$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, 23w - 156]$ | $-1$ |
$3$ | $[3, 3, -w - 7]$ | $-1$ |