Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, -2w + 19]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $90$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 5x^{6} + 24x^{4} + 5x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-e^{7} - 5e^{5} - 24e^{3} - 5e$ |
| 3 | $[3, 3, -2w + 19]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w]$ | $-\frac{19}{24}e^{7} - 4e^{5} - 19e^{3} - \frac{95}{24}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{1}{24}e^{7} - \frac{91}{24}e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{23}{24}e^{6} + 5e^{4} + 23e^{2} + \frac{115}{24}$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{25}{24}e^{6} + 5e^{4} + 23e^{2} + \frac{5}{24}$ |
| 17 | $[17, 17, w + 3]$ | $-\frac{3}{8}e^{7} - 2e^{5} - 9e^{3} - \frac{15}{8}e$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{107}{8}e$ |
| 19 | $[19, 19, w + 6]$ | $-\frac{25}{24}e^{6} - 5e^{4} - 25e^{2} - \frac{5}{24}$ |
| 19 | $[19, 19, w + 12]$ | $\phantom{-}\frac{25}{24}e^{6} + 5e^{4} + 25e^{2} + \frac{125}{24}$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}\frac{35}{24}e^{6} + 7e^{4} + 33e^{2} + \frac{7}{24}$ |
| 37 | $[37, 37, w + 34]$ | $\phantom{-}\frac{13}{24}e^{6} + 3e^{4} + 13e^{2} + \frac{65}{24}$ |
| 49 | $[49, 7, -7]$ | $-12$ |
| 59 | $[59, 59, -4w - 33]$ | $-\frac{15}{4}e^{7} - 18e^{5} - 86e^{3} - \frac{3}{4}e$ |
| 59 | $[59, 59, 4w - 37]$ | $\phantom{-}\frac{5}{4}e^{7} + 6e^{5} + 28e^{3} + \frac{1}{4}e$ |
| 61 | $[61, 61, w + 28]$ | $-\frac{43}{24}e^{6} - 9e^{4} - 43e^{2} - \frac{215}{24}$ |
| 61 | $[61, 61, w + 32]$ | $-\frac{5}{24}e^{6} - e^{4} - 3e^{2} - \frac{1}{24}$ |
| 71 | $[71, 71, w + 22]$ | $\phantom{-}\frac{59}{24}e^{7} + 12e^{5} + 59e^{3} + \frac{295}{24}e$ |
| 71 | $[71, 71, w + 48]$ | $\phantom{-}\frac{7}{24}e^{7} - \frac{829}{24}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w + 19]$ | $-1$ |