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:
| \(x^{8} - 17x^{6} + 102x^{4} - 252x^{2} + 215\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 160]$ | $-e$ |
| 2 | $[2, 2, -17w + 177]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -842w + 8767]$ | $-1$ |
| 7 | $[7, 7, -2w + 21]$ | $\phantom{-}e^{6} - 10e^{4} + 27e^{2} - 18$ |
| 7 | $[7, 7, 2w + 19]$ | $\phantom{-}e^{6} - 10e^{4} + 27e^{2} - 18$ |
| 13 | $[13, 13, -12w - 113]$ | $-e^{6} + 13e^{4} - 53e^{2} + 66$ |
| 13 | $[13, 13, 12w - 125]$ | $-e^{6} + 13e^{4} - 53e^{2} + 66$ |
| 17 | $[17, 17, 182w - 1895]$ | $-e^{7} + 13e^{5} - 53e^{3} + 65e$ |
| 17 | $[17, 17, 182w + 1713]$ | $\phantom{-}e^{7} - 13e^{5} + 53e^{3} - 65e$ |
| 23 | $[23, 23, -512w - 4819]$ | $-e^{5} + 8e^{3} - 12e$ |
| 23 | $[23, 23, 512w - 5331]$ | $\phantom{-}e^{5} - 8e^{3} + 12e$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}3e^{6} - 37e^{4} + 140e^{2} - 161$ |
| 29 | $[29, 29, 22w - 229]$ | $-2e^{5} + 17e^{3} - 31e$ |
| 29 | $[29, 29, 22w + 207]$ | $\phantom{-}2e^{5} - 17e^{3} + 31e$ |
| 43 | $[43, 43, 114w + 1073]$ | $\phantom{-}e^{4} - 6e^{2} + 6$ |
| 43 | $[43, 43, 114w - 1187]$ | $\phantom{-}e^{4} - 6e^{2} + 6$ |
| 47 | $[47, 47, 8w - 83]$ | $-e$ |
| 47 | $[47, 47, -8w - 75]$ | $\phantom{-}e$ |
| 61 | $[61, 61, -1172w - 11031]$ | $\phantom{-}e^{6} - 11e^{4} + 36e^{2} - 42$ |
| 61 | $[61, 61, 1172w - 12203]$ | $\phantom{-}e^{6} - 11e^{4} + 36e^{2} - 42$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -842w + 8767]$ | $1$ |