Base field \(\Q(\sqrt{114}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 114\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 14x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -3w - 32]$ | $\phantom{-}0$ |
3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{11}{6}e$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 3]$ | $-\frac{1}{3}e^{3} + \frac{14}{3}e$ |
7 | $[7, 7, -w + 11]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}$ |
7 | $[7, 7, w + 11]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{9}{2}$ |
11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{17}{6}e$ |
11 | $[11, 11, w + 9]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{17}{6}e$ |
13 | $[13, 13, w + 6]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{23}{6}e$ |
13 | $[13, 13, w + 7]$ | $-\frac{1}{2}e^{3} + \frac{15}{2}e$ |
19 | $[19, 19, w]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e$ |
37 | $[37, 37, w + 15]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{15}{2}e$ |
37 | $[37, 37, w + 22]$ | $-\frac{1}{6}e^{3} + \frac{23}{6}e$ |
41 | $[41, 41, 37w + 395]$ | $-\frac{1}{2}e^{2} - \frac{9}{2}$ |
41 | $[41, 41, 5w + 53]$ | $-\frac{1}{2}e^{2} + \frac{23}{2}$ |
67 | $[67, 67, w + 28]$ | $\phantom{-}0$ |
67 | $[67, 67, w + 39]$ | $\phantom{-}0$ |
71 | $[71, 71, 40w + 427]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}$ |
71 | $[71, 71, 8w + 85]$ | $-\frac{1}{2}e^{2} + \frac{11}{2}$ |
73 | $[73, 73, -2w + 23]$ | $-e^{2} + 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -3w - 32]$ | $-1$ |