Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, w^{2} - 3w - 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 4x^{3} - 2x^{2} + 18x - 14\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-e^{3} + 2e^{2} + 5e - 5$ |
| 7 | $[7, 7, w - 3]$ | $-e^{3} + 2e^{2} + 6e - 8$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{3} - 3e^{2} - 4e + 11$ |
| 9 | $[9, 3, w^{2} - 3w - 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w + 3]$ | $-2e^{3} + 6e^{2} + 10e - 23$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}4e^{3} - 10e^{2} - 23e + 41$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}2e^{3} - 6e^{2} - 10e + 22$ |
| 23 | $[23, 23, w^{2} - 4w + 1]$ | $\phantom{-}e^{3} - 2e^{2} - 6e + 8$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $\phantom{-}6e^{3} - 15e^{2} - 33e + 61$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-e^{3} + 3e^{2} + 7e - 14$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}4e^{3} - 9e^{2} - 23e + 35$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-2e^{3} + 5e^{2} + 10e - 14$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-8e^{3} + 21e^{2} + 47e - 87$ |
| 41 | $[41, 41, w^{2} - w - 10]$ | $-4e^{3} + 10e^{2} + 25e - 45$ |
| 43 | $[43, 43, -2w - 3]$ | $-7e^{3} + 19e^{2} + 39e - 68$ |
| 47 | $[47, 47, -w^{2} - w + 4]$ | $-3e^{2} + 3e + 14$ |
| 49 | $[49, 7, -w^{2} + 5w - 5]$ | $-4e^{3} + 9e^{2} + 22e - 29$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}5e^{3} - 13e^{2} - 31e + 58$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-10e^{3} + 26e^{2} + 55e - 102$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w^{2} - 3w - 2]$ | $-1$ |