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: | $[5, 5, w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $168$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 3x^{4} + 2x^{3} + 9x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{2}{3}e^{5} - \frac{5}{3}e^{3} - \frac{5}{3}e^{2} - 5e - \frac{5}{3}$ |
| 3 | $[3, 3, -2w + 19]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} + e^{2} + \frac{1}{3}e + \frac{2}{3}$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{3}e^{5} - e^{3} - \frac{1}{3}e^{2} - 3e - 1$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{5}{3}e^{5} + e^{4} - 5e^{3} - \frac{5}{3}e^{2} - 13e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}e^{5} - \frac{1}{3}e^{4} + 3e^{3} + e^{2} + \frac{23}{3}e$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{4}{3}e^{5} - 3e^{3} - \frac{7}{3}e^{2} - 9e - 3$ |
| 17 | $[17, 17, w + 3]$ | $-e^{5} - \frac{11}{3}e^{3} - 3e^{2} - 11e - \frac{11}{3}$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}\frac{2}{3}e^{5} - \frac{1}{3}e^{4} + 2e^{3} + \frac{2}{3}e^{2} + \frac{14}{3}e$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{5}{3}e^{3} + \frac{1}{3}e^{2} + 5e + \frac{5}{3}$ |
| 19 | $[19, 19, w + 12]$ | $-\frac{8}{3}e^{5} + \frac{4}{3}e^{4} - 8e^{3} - \frac{8}{3}e^{2} - \frac{56}{3}e$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}\frac{2}{3}e^{5} + \frac{1}{3}e^{3} + \frac{2}{3}e^{2} + e + \frac{1}{3}$ |
| 37 | $[37, 37, w + 34]$ | $\phantom{-}\frac{13}{3}e^{5} - \frac{8}{3}e^{4} + 13e^{3} + \frac{13}{3}e^{2} + \frac{100}{3}e$ |
| 49 | $[49, 7, -7]$ | $-\frac{1}{3}e^{4} - e^{2} - \frac{1}{3}e - 7$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}\frac{5}{3}e^{4} - \frac{2}{3}e^{3} + 5e^{2} + \frac{5}{3}e + \frac{13}{3}$ |
| 59 | $[59, 59, 4w - 37]$ | $-\frac{5}{3}e^{4} + 2e^{3} - 5e^{2} - \frac{5}{3}e - 7$ |
| 61 | $[61, 61, w + 28]$ | $\phantom{-}\frac{7}{3}e^{5} - \frac{2}{3}e^{4} + 7e^{3} + \frac{7}{3}e^{2} + \frac{73}{3}e$ |
| 61 | $[61, 61, w + 32]$ | $-\frac{5}{3}e^{5} - \frac{8}{3}e^{3} - \frac{11}{3}e^{2} - 8e - \frac{8}{3}$ |
| 71 | $[71, 71, w + 22]$ | $\phantom{-}e^{5} + 4e^{3} + 12e + 4$ |
| 71 | $[71, 71, w + 48]$ | $-\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - e^{3} - \frac{1}{3}e^{2} - \frac{19}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $\frac{1}{3}e^{5} + e^{3} + \frac{1}{3}e^{2} + 3e + 1$ |