Base field \(\Q(\sqrt{95}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 95\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 22x^{2} + 49\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{42}e^{3} + \frac{29}{42}e$ |
| 5 | $[5, 5, -w + 10]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}\frac{1}{7}e^{3} + \frac{22}{7}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{1}{14}e^{3} + \frac{1}{14}e$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{3}{14}e^{3} - \frac{59}{14}e$ |
| 19 | $[19, 19, 2w - 19]$ | $-2$ |
| 23 | $[23, 23, w + 7]$ | $\phantom{-}\frac{2}{7}e^{3} + \frac{37}{7}e$ |
| 23 | $[23, 23, w + 16]$ | $-\frac{1}{7}e^{3} - \frac{8}{7}e$ |
| 31 | $[31, 31, -w - 8]$ | $-6$ |
| 31 | $[31, 31, w - 8]$ | $-6$ |
| 37 | $[37, 37, w + 13]$ | $\phantom{-}\frac{1}{7}e^{3} + \frac{1}{7}e$ |
| 37 | $[37, 37, w + 24]$ | $-\frac{3}{7}e^{3} - \frac{59}{7}e$ |
| 43 | $[43, 43, w + 3]$ | $-\frac{2}{7}e^{3} - \frac{30}{7}e$ |
| 43 | $[43, 43, w + 40]$ | $\phantom{-}\frac{2}{7}e^{3} + \frac{30}{7}e$ |
| 47 | $[47, 47, w + 1]$ | $-\frac{1}{7}e^{3} - \frac{29}{7}e$ |
| 47 | $[47, 47, w + 46]$ | $-\frac{1}{7}e^{3} - \frac{29}{7}e$ |
| 53 | $[53, 53, w + 25]$ | $-\frac{5}{14}e^{3} - \frac{61}{14}e$ |
| 53 | $[53, 53, w + 28]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{17}{2}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $-\frac{1}{42}e^{3} - \frac{29}{42}e$ |