Base field \(\Q(\sqrt{185}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 46\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, 2w]$ |
| 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:
| \(x^{6} + 27x^{4} + 189x^{2} + 324\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{54}e^{5} - \frac{7}{18}e^{3} - \frac{3}{2}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{3}e^{2} - 2$ |
| 11 | $[11, 11, 2w + 13]$ | $\phantom{-}\frac{1}{9}e^{4} + \frac{8}{3}e^{2} + 12$ |
| 11 | $[11, 11, -2w + 15]$ | $\phantom{-}\frac{1}{9}e^{4} + \frac{5}{3}e^{2}$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{2}{27}e^{5} + \frac{5}{3}e^{3} + 8e$ |
| 13 | $[13, 13, w + 8]$ | $\phantom{-}\frac{1}{27}e^{5} + \frac{2}{3}e^{3} + 2e$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}\frac{1}{3}e^{3} + 4e$ |
| 23 | $[23, 23, w]$ | $\phantom{-}2e$ |
| 23 | $[23, 23, w + 22]$ | $\phantom{-}\frac{1}{3}e^{3} + 5e$ |
| 37 | $[37, 37, w + 18]$ | $-\frac{1}{9}e^{5} - \frac{8}{3}e^{3} - 13e$ |
| 41 | $[41, 41, -2w + 13]$ | $-\frac{1}{9}e^{4} - \frac{8}{3}e^{2} - 6$ |
| 41 | $[41, 41, -2w - 11]$ | $-\frac{1}{9}e^{4} - \frac{5}{3}e^{2} - 6$ |
| 43 | $[43, 43, w + 11]$ | $\phantom{-}\frac{4}{27}e^{5} + 3e^{3} + 10e$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{4}{27}e^{5} - \frac{10}{3}e^{3} - 13e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{9}e^{4} + 2e^{2} + 2$ |
| 71 | $[71, 71, -2w + 17]$ | $\phantom{-}\frac{4}{9}e^{4} + \frac{29}{3}e^{2} + 36$ |
| 71 | $[71, 71, -2w - 15]$ | $\phantom{-}\frac{1}{9}e^{4} + \frac{8}{3}e^{2} + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |
| $2$ | $[2, 2, w + 1]$ | $\frac{1}{54}e^{5} + \frac{7}{18}e^{3} + \frac{3}{2}e$ |