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:
| \(x^{8} + 11x^{6} + 92x^{4} + 319x^{2} + 841\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{11}{2668}e^{7} + \frac{1}{29}e^{5} + \frac{11}{29}e^{3} + \frac{121}{92}e$ |
| 3 | $[3, 3, -2w + 19]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{37}{2668}e^{7} + \frac{6}{29}e^{5} + \frac{37}{29}e^{3} + \frac{407}{92}e$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{1}{92}e^{7} + \frac{233}{92}e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{137}{2668}e^{6} + \frac{23}{29}e^{4} + \frac{137}{29}e^{2} + \frac{1507}{92}$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{11}{116}e^{6} - \frac{23}{29}e^{4} - \frac{137}{29}e^{2} - \frac{29}{4}$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}\frac{37}{2668}e^{7} + \frac{6}{29}e^{5} + \frac{37}{29}e^{3} + \frac{407}{92}e$ |
| 17 | $[17, 17, w + 13]$ | $-\frac{1}{92}e^{7} + \frac{233}{92}e$ |
| 19 | $[19, 19, w + 6]$ | $-\frac{121}{2668}e^{6} - \frac{11}{29}e^{4} - \frac{63}{29}e^{2} - \frac{319}{92}$ |
| 19 | $[19, 19, w + 12]$ | $\phantom{-}\frac{63}{2668}e^{6} + \frac{11}{29}e^{4} + \frac{63}{29}e^{2} + \frac{693}{92}$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}\frac{55}{2668}e^{6} + \frac{5}{29}e^{4} + \frac{55}{29}e^{2} + \frac{145}{92}$ |
| 37 | $[37, 37, w + 34]$ | $-\frac{55}{2668}e^{6} - \frac{5}{29}e^{4} - \frac{55}{29}e^{2} - \frac{605}{92}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}14$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}\frac{11}{667}e^{7} + \frac{4}{29}e^{5} + \frac{44}{29}e^{3} + \frac{29}{23}e$ |
| 59 | $[59, 59, 4w - 37]$ | $-\frac{11}{667}e^{7} - \frac{4}{29}e^{5} - \frac{44}{29}e^{3} - \frac{29}{23}e$ |
| 61 | $[61, 61, w + 28]$ | $-\frac{137}{2668}e^{6} - \frac{23}{29}e^{4} - \frac{137}{29}e^{2} - \frac{1507}{92}$ |
| 61 | $[61, 61, w + 32]$ | $\phantom{-}\frac{11}{116}e^{6} + \frac{23}{29}e^{4} + \frac{137}{29}e^{2} + \frac{29}{4}$ |
| 71 | $[71, 71, w + 22]$ | $-\frac{89}{2668}e^{7} - \frac{16}{29}e^{5} - \frac{89}{29}e^{3} - \frac{979}{92}e$ |
| 71 | $[71, 71, w + 48]$ | $\phantom{-}\frac{3}{92}e^{7} - \frac{515}{92}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w + 19]$ | $1$ |