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: | $[4,4,-w + 1]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 12x^{6} + 39x^{4} - 36x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -2w + 19]$ | $-\frac{1}{3}e^{6} + \frac{11}{3}e^{4} - 10e^{2} + 5$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{3}e^{5} - 3e^{3} + 4e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{11}{3}e^{5} + 9e^{3} - e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{1}{3}e^{6} - 4e^{4} + 12e^{2} - 7$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{1}{3}e^{6} + 4e^{4} - 12e^{2} + 5$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}\frac{2}{3}e^{7} - \frac{25}{3}e^{5} + 28e^{3} - 22e$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}e^{7} - \frac{34}{3}e^{5} + 31e^{3} - 12e$ |
| 19 | $[19, 19, w + 6]$ | $-\frac{5}{3}e^{6} + 19e^{4} - 53e^{2} + 26$ |
| 19 | $[19, 19, w + 12]$ | $-\frac{1}{3}e^{6} + 3e^{4} - 3e^{2} - 4$ |
| 37 | $[37, 37, w + 2]$ | $-\frac{2}{3}e^{6} + 8e^{4} - 25e^{2} + 11$ |
| 37 | $[37, 37, w + 34]$ | $\phantom{-}\frac{2}{3}e^{6} - 8e^{4} + 25e^{2} - 13$ |
| 49 | $[49, 7, -7]$ | $-\frac{4}{3}e^{6} + 14e^{4} - 34e^{2} + 11$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}\frac{2}{3}e^{7} - \frac{25}{3}e^{5} + 29e^{3} - 28e$ |
| 59 | $[59, 59, 4w - 37]$ | $-\frac{1}{3}e^{7} + \frac{11}{3}e^{5} - 9e^{3} - e$ |
| 61 | $[61, 61, w + 28]$ | $\phantom{-}\frac{7}{3}e^{6} - 25e^{4} + 62e^{2} - 25$ |
| 61 | $[61, 61, w + 32]$ | $-\frac{7}{3}e^{6} + 27e^{4} - 78e^{2} + 35$ |
| 71 | $[71, 71, w + 22]$ | $-\frac{11}{3}e^{7} + \frac{127}{3}e^{5} - 123e^{3} + 69e$ |
| 71 | $[71, 71, w + 48]$ | $\phantom{-}\frac{1}{3}e^{5} - 3e^{3} + 4e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $-1$ |