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: | $[4, 2, -w^{2} + w + 5]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 2x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} + 2w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 3]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + w + 5]$ | $-1$ |
| 9 | $[9, 3, w^{2} + 2w - 1]$ | $\phantom{-}3e^{2} + 5e - 2$ |
| 11 | $[11, 11, w + 1]$ | $-3e^{2} - 4e + 3$ |
| 13 | $[13, 13, -2w^{2} - 3w + 5]$ | $-e - 3$ |
| 17 | $[17, 17, -2w + 5]$ | $-3e^{2} - 5e + 2$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}e^{2} - 1$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $-e^{2} + e + 2$ |
| 29 | $[29, 29, 3w^{2} + 6w - 5]$ | $\phantom{-}3e^{2} + 5e - 7$ |
| 37 | $[37, 37, 4w^{2} - 2w - 25]$ | $-3e^{2} - 8e$ |
| 67 | $[67, 67, 2w^{2} + 2w - 7]$ | $\phantom{-}4e$ |
| 67 | $[67, 67, -2w^{2} - 5w + 1]$ | $\phantom{-}2e^{2} - 9$ |
| 67 | $[67, 67, 2w^{2} + 3w - 7]$ | $-2e^{2} - 9e + 3$ |
| 71 | $[71, 71, w - 5]$ | $\phantom{-}7e^{2} + 13e - 8$ |
| 73 | $[73, 73, w^{2} + 2w - 5]$ | $-e^{2} - 9e - 7$ |
| 73 | $[73, 73, 2w^{2} - w - 11]$ | $-7e^{2} - 18e + 5$ |
| 73 | $[73, 73, -2w - 1]$ | $\phantom{-}7e + 3$ |
| 83 | $[83, 83, 4w^{2} - 31]$ | $\phantom{-}e^{2} + 2e - 3$ |
| 97 | $[97, 97, 2w^{2} + 2w - 5]$ | $-7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{2} + w + 5]$ | $1$ |