Base field 3.3.1229.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[12, 6, w^{2} + w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 6x^{2} - 4x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} + 2w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 3]$ | $-1$ |
| 4 | $[4, 2, -w^{2} + w + 5]$ | $-1$ |
| 9 | $[9, 3, w^{2} + 2w - 1]$ | $\phantom{-}e + 1$ |
| 11 | $[11, 11, w + 1]$ | $-e^{3} - e^{2} + 5e + 1$ |
| 13 | $[13, 13, -2w^{2} - 3w + 5]$ | $\phantom{-}e^{3} - e^{2} - 5e + 3$ |
| 17 | $[17, 17, -2w + 5]$ | $\phantom{-}e^{3} + e^{2} - 6e - 2$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}e^{3} - 6e - 3$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 6$ |
| 29 | $[29, 29, 3w^{2} + 6w - 5]$ | $-2e^{2} - 4e + 8$ |
| 37 | $[37, 37, 4w^{2} - 2w - 25]$ | $-2e^{3} - e^{2} + 10e - 1$ |
| 67 | $[67, 67, 2w^{2} + 2w - 7]$ | $-2e^{3} + e^{2} + 9e - 8$ |
| 67 | $[67, 67, -2w^{2} - 5w + 1]$ | $\phantom{-}2e + 2$ |
| 67 | $[67, 67, 2w^{2} + 3w - 7]$ | $-e^{3} + 5e - 8$ |
| 71 | $[71, 71, w - 5]$ | $-2e^{3} - 3e^{2} + 9e + 8$ |
| 73 | $[73, 73, w^{2} + 2w - 5]$ | $-e^{3} - 4e^{2} + 7e + 12$ |
| 73 | $[73, 73, 2w^{2} - w - 11]$ | $\phantom{-}3e^{2} + 4e - 9$ |
| 73 | $[73, 73, -2w - 1]$ | $-2e^{3} - 2e^{2} + 8e - 2$ |
| 83 | $[83, 83, 4w^{2} - 31]$ | $-e + 1$ |
| 97 | $[97, 97, 2w^{2} + 2w - 5]$ | $-2e^{3} + 4e^{2} + 10e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 3]$ | $1$ |
| $4$ | $[4, 2, -w^{2} + w + 5]$ | $1$ |