Base field 3.3.1436.1
Generator \(w\), with minimal polynomial \(x^{3} - 11x - 12\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[3, 3, w^{2} - w - 9]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 6x^{2} + 7x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e^{3} - 5e + 2$ |
| 3 | $[3, 3, w^{2} - w - 9]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{2} + 3w + 5]$ | $-e^{3} + 5e$ |
| 11 | $[11, 11, -w^{2} + w + 11]$ | $\phantom{-}e^{3} - 5e$ |
| 13 | $[13, 13, 2w^{2} - 4w - 13]$ | $-e^{3} + 7e - 2$ |
| 23 | $[23, 23, -w^{2} + w + 7]$ | $\phantom{-}e^{3} + e^{2} - 3e - 3$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $-e^{3} - e^{2} + 5e + 7$ |
| 41 | $[41, 41, -2w^{2} + 2w + 19]$ | $\phantom{-}2e^{3} + 2e^{2} - 10e$ |
| 41 | $[41, 41, w^{2} - 3w - 7]$ | $-2e^{3} - 3e^{2} + 10e + 5$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-2e + 4$ |
| 47 | $[47, 47, 3w^{2} - 7w - 17]$ | $-4e^{3} + 18e - 8$ |
| 53 | $[53, 53, -2w - 1]$ | $\phantom{-}3e^{3} + e^{2} - 13e + 3$ |
| 61 | $[61, 61, -2w + 7]$ | $-2e^{3} - 3e^{2} + 10e + 3$ |
| 67 | $[67, 67, 3w^{2} - 5w - 23]$ | $\phantom{-}3e^{3} + 2e^{2} - 17e - 2$ |
| 67 | $[67, 67, 2w^{2} - 4w - 11]$ | $-3e^{3} - 3e^{2} + 13e + 5$ |
| 67 | $[67, 67, 3w^{2} - 7w - 13]$ | $-e^{3} + 3e^{2} + 5e - 13$ |
| 79 | $[79, 79, w^{2} + w - 5]$ | $\phantom{-}2e^{3} - e^{2} - 14e + 11$ |
| 89 | $[89, 89, 5w^{2} - 7w - 47]$ | $-e^{3} + 5e^{2} + 7e - 15$ |
| 97 | $[97, 97, 5w^{2} - 11w - 29]$ | $-e^{3} - 2e^{2} + 5e + 18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{2} - w - 9]$ | $-1$ |