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: | $[3, 3, -842w + 8767]$ |
| 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:
| \(x^{8} - 10x^{6} + 24x^{4} - 10x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 160]$ | $-e^{7} + 10e^{5} - 24e^{3} + 10e$ |
| 2 | $[2, 2, -17w + 177]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -842w + 8767]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -2w + 21]$ | $-e^{6} + 9e^{4} - 16e^{2}$ |
| 7 | $[7, 7, 2w + 19]$ | $\phantom{-}2e^{6} - 19e^{4} + 39e^{2} - 6$ |
| 13 | $[13, 13, -12w - 113]$ | $\phantom{-}e^{2} - 4$ |
| 13 | $[13, 13, 12w - 125]$ | $-e^{6} + 10e^{4} - 24e^{2} + 6$ |
| 17 | $[17, 17, 182w - 1895]$ | $\phantom{-}7e^{7} - 69e^{5} + 157e^{3} - 40e$ |
| 17 | $[17, 17, 182w + 1713]$ | $\phantom{-}4e^{7} - 39e^{5} + 85e^{3} - 13e$ |
| 23 | $[23, 23, -512w - 4819]$ | $\phantom{-}e^{7} - 11e^{5} + 32e^{3} - 22e$ |
| 23 | $[23, 23, 512w - 5331]$ | $\phantom{-}8e^{7} - 78e^{5} + 173e^{3} - 43e$ |
| 25 | $[25, 5, -5]$ | $-e^{6} + 10e^{4} - 23e^{2} + 4$ |
| 29 | $[29, 29, 22w - 229]$ | $-7e^{7} + 69e^{5} - 158e^{3} + 43e$ |
| 29 | $[29, 29, 22w + 207]$ | $\phantom{-}3e^{7} - 30e^{5} + 73e^{3} - 33e$ |
| 43 | $[43, 43, 114w + 1073]$ | $-4e^{6} + 39e^{4} - 85e^{2} + 12$ |
| 43 | $[43, 43, 114w - 1187]$ | $-e^{6} + 11e^{4} - 30e^{2} + 6$ |
| 47 | $[47, 47, 8w - 83]$ | $-9e^{7} + 89e^{5} - 203e^{3} + 51e$ |
| 47 | $[47, 47, -8w - 75]$ | $-15e^{7} + 147e^{5} - 329e^{3} + 77e$ |
| 61 | $[61, 61, -1172w - 11031]$ | $-e^{4} + 6e^{2} - 8$ |
| 61 | $[61, 61, 1172w - 12203]$ | $\phantom{-}4e^{6} - 39e^{4} + 86e^{2} - 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -842w + 8767]$ | $-1$ |