Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, w^{2} + w - 8]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 27x^{4} + 84x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $-\frac{2}{51}e^{4} + \frac{41}{51}e^{2} - \frac{29}{51}$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 11]$ | $\phantom{-}\frac{2}{51}e^{4} - \frac{41}{51}e^{2} - \frac{22}{51}$ |
| 7 | $[7, 7, -w^{2} + 9]$ | $\phantom{-}\frac{11}{51}e^{5} - \frac{302}{51}e^{3} + \frac{1001}{51}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{2}{51}e^{4} + \frac{41}{51}e^{2} - \frac{131}{51}$ |
| 13 | $[13, 13, -w]$ | $\phantom{-}\frac{13}{51}e^{5} - \frac{343}{51}e^{3} + \frac{877}{51}e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{2}{17}e^{5} + \frac{58}{17}e^{3} - \frac{233}{17}e$ |
| 23 | $[23, 23, w^{2} + w - 10]$ | $\phantom{-}\frac{1}{17}e^{4} - \frac{29}{17}e^{2} + \frac{57}{17}$ |
| 29 | $[29, 29, 2w^{2} - 21]$ | $-\frac{13}{51}e^{5} + \frac{343}{51}e^{3} - \frac{928}{51}e$ |
| 37 | $[37, 37, 2w^{2} + w - 17]$ | $-\frac{8}{51}e^{5} + \frac{215}{51}e^{3} - \frac{677}{51}e$ |
| 43 | $[43, 43, 3w^{2} + 3w - 22]$ | $-\frac{5}{51}e^{5} + \frac{128}{51}e^{3} - \frac{251}{51}e$ |
| 47 | $[47, 47, w^{2} - 6]$ | $\phantom{-}\frac{23}{51}e^{5} - \frac{599}{51}e^{3} + \frac{1532}{51}e$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{32}{51}e^{5} + \frac{860}{51}e^{3} - \frac{2657}{51}e$ |
| 47 | $[47, 47, -w^{2} + 12]$ | $-\frac{4}{17}e^{4} + \frac{99}{17}e^{2} - \frac{194}{17}$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-\frac{26}{51}e^{5} + \frac{686}{51}e^{3} - \frac{1856}{51}e$ |
| 61 | $[61, 61, w^{2} - 5]$ | $-\frac{29}{51}e^{5} + \frac{773}{51}e^{3} - \frac{2231}{51}e$ |
| 67 | $[67, 67, w^{2} - w - 7]$ | $\phantom{-}\frac{8}{51}e^{5} - \frac{215}{51}e^{3} + \frac{677}{51}e$ |
| 73 | $[73, 73, 7w^{2} + 3w - 66]$ | $\phantom{-}\frac{16}{51}e^{4} - \frac{379}{51}e^{2} + \frac{589}{51}$ |
| 79 | $[79, 79, 2w^{2} - 19]$ | $\phantom{-}\frac{5}{51}e^{5} - \frac{128}{51}e^{3} + \frac{251}{51}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $1$ |