Base field \(\Q(\zeta_{7})^+\)
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[167, 167, w^{2} + w - 8]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - x^{2} - 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, 2w^{2} - w - 3]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}2e^{2} - 4e - 4$ |
| 13 | $[13, 13, -w^{2} - w + 3]$ | $\phantom{-}2e - 2$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-e^{2} - e + 3$ |
| 13 | $[13, 13, -2w^{2} + w + 2]$ | $-3e^{2} + 4e + 8$ |
| 27 | $[27, 3, 3]$ | $-3e^{2} + 6e + 6$ |
| 29 | $[29, 29, 3w^{2} - 2w - 4]$ | $\phantom{-}4e^{2} - 6e - 12$ |
| 29 | $[29, 29, 2w^{2} + w - 4]$ | $-e^{2} + e + 3$ |
| 29 | $[29, 29, -w^{2} + 3w + 1]$ | $\phantom{-}4e - 2$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}3e^{2} - 7e - 11$ |
| 41 | $[41, 41, 2w^{2} - 3w - 4]$ | $\phantom{-}4e^{2} - 5e - 8$ |
| 41 | $[41, 41, -3w^{2} + w + 3]$ | $-2e^{2} + 4$ |
| 43 | $[43, 43, w^{2} + 2w - 5]$ | $-2e^{2} + 6$ |
| 43 | $[43, 43, 2w^{2} + w - 5]$ | $\phantom{-}4e^{2} - 4e - 14$ |
| 43 | $[43, 43, 3w^{2} - 2w - 3]$ | $-6e^{2} + 10e + 16$ |
| 71 | $[71, 71, 4w^{2} - 3w - 5]$ | $-5e^{2} + 6e + 12$ |
| 71 | $[71, 71, 3w^{2} - 4w - 5]$ | $\phantom{-}3e^{2} - 5e + 3$ |
| 71 | $[71, 71, -4w^{2} + w + 5]$ | $-2e^{2} + 4e + 2$ |
| 83 | $[83, 83, w^{2} + w - 7]$ | $\phantom{-}2e^{2} - 4e - 12$ |
| 83 | $[83, 83, w^{2} - 2w - 6]$ | $\phantom{-}4e^{2} + e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $167$ | $[167, 167, w^{2} + w - 8]$ | $-1$ |