Base field 3.3.1772.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x + 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 9, w^{2} - 5w + 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 7x^{4} + 11x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w^{2} + 11]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{3} + \frac{9}{2}e$ |
| 3 | $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ | $\phantom{-}e^{4} - 6e^{2} + 4$ |
| 9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{5}{2}w - 1]$ | $\phantom{-}e^{3} - 4e$ |
| 25 | $[25, 5, \frac{7}{2}w^{2} - \frac{31}{2}w + 9]$ | $-2e^{5} + 12e^{3} - 8e$ |
| 29 | $[29, 29, -\frac{5}{2}w^{2} + \frac{1}{2}w + 29]$ | $\phantom{-}e^{4} - 6e^{2} + 2$ |
| 41 | $[41, 41, -w^{2} + 3w - 1]$ | $\phantom{-}4e^{5} - 24e^{3} + 22e$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - \frac{3}{2}w + 3]$ | $-2e^{5} + 11e^{3} - 10e$ |
| 41 | $[41, 41, 2w + 7]$ | $\phantom{-}0$ |
| 43 | $[43, 43, -\frac{7}{2}w^{2} - \frac{1}{2}w + 37]$ | $-e^{5} + 3e^{3} + 6e$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{9}{2}w + 3]$ | $-3e^{4} + 18e^{2} - 16$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{1}{2}w + 1]$ | $\phantom{-}e^{5} - 6e^{3} + e$ |
| 47 | $[47, 47, -w^{2} + w + 15]$ | $\phantom{-}e^{4} - 5e^{2}$ |
| 53 | $[53, 53, -2w^{2} + 2w + 29]$ | $-7e^{4} + 41e^{2} - 34$ |
| 59 | $[59, 59, w^{2} - w - 13]$ | $-2e^{3} + 7e$ |
| 67 | $[67, 67, -\frac{1}{2}w^{2} + \frac{1}{2}w + 9]$ | $\phantom{-}e^{5} - 7e^{3} + 5e$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}2e^{4} - 9e^{2}$ |
| 73 | $[73, 73, \frac{3}{2}w^{2} - \frac{11}{2}w + 1]$ | $-3e^{5} + 20e^{3} - 24e$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} + \frac{15}{2}w - 5]$ | $-e^{4} + e^{2} + 4$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.