Base field \(\Q(\sqrt{393}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 98\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $104$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 12x^{6} + 46x^{4} - 56x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 160]$ | $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} + 8e$ |
| 2 | $[2, 2, -17w + 177]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -842w + 8767]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -2w + 21]$ | $-e^{4} + 5e^{2} - 3$ |
| 7 | $[7, 7, 2w + 19]$ | $\phantom{-}\frac{1}{2}e^{6} - 3e^{4} + 3e^{2} - 1$ |
| 13 | $[13, 13, -12w - 113]$ | $\phantom{-}\frac{1}{2}e^{6} - 4e^{4} + 7e^{2} + 3$ |
| 13 | $[13, 13, 12w - 125]$ | $\phantom{-}e^{2} - 1$ |
| 17 | $[17, 17, 182w - 1895]$ | $-\frac{1}{2}e^{7} + 6e^{5} - 21e^{3} + 19e$ |
| 17 | $[17, 17, 182w + 1713]$ | $-\frac{1}{2}e^{7} + \frac{7}{2}e^{5} - 6e^{3} + 4e$ |
| 23 | $[23, 23, -512w - 4819]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{11}{2}e^{5} + 20e^{3} - 24e$ |
| 23 | $[23, 23, 512w - 5331]$ | $\phantom{-}\frac{1}{2}e^{7} - 4e^{5} + 7e^{3} + e$ |
| 25 | $[25, 5, -5]$ | $-\frac{1}{2}e^{6} + 4e^{4} - 8e^{2} + 2$ |
| 29 | $[29, 29, 22w - 229]$ | $-\frac{1}{2}e^{7} + \frac{3}{2}e^{5} + 11e^{3} - 31e$ |
| 29 | $[29, 29, 22w + 207]$ | $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - 26e^{3} + 27e$ |
| 43 | $[43, 43, 114w + 1073]$ | $-\frac{5}{2}e^{6} + 20e^{4} - 37e^{2} + 1$ |
| 43 | $[43, 43, 114w - 1187]$ | $-e^{6} + 8e^{4} - 19e^{2} + 13$ |
| 47 | $[47, 47, 8w - 83]$ | $\phantom{-}2e^{5} - 13e^{3} + 15e$ |
| 47 | $[47, 47, -8w - 75]$ | $-\frac{5}{2}e^{5} + 17e^{3} - 24e$ |
| 61 | $[61, 61, -1172w - 11031]$ | $-2e^{6} + 17e^{4} - 35e^{2} + 1$ |
| 61 | $[61, 61, 1172w - 12203]$ | $-\frac{3}{2}e^{6} + 11e^{4} - 21e^{2} + 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -842w + 8767]$ | $-1$ |