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: | $[239, 239, 6w^{2} - 5w - 7]$ |
| 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:
| \(x^{3} - 12x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, 2w^{2} - w - 3]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-e$ |
| 13 | $[13, 13, -w^{2} - w + 3]$ | $\phantom{-}\frac{3}{4}e^{2} - \frac{3}{2}e - 5$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-\frac{1}{2}e^{2} + e + 4$ |
| 13 | $[13, 13, -2w^{2} + w + 2]$ | $-\frac{1}{2}e + 1$ |
| 27 | $[27, 3, 3]$ | $-\frac{3}{4}e^{2} + 2e + 9$ |
| 29 | $[29, 29, 3w^{2} - 2w - 4]$ | $\phantom{-}e^{2} + e - 8$ |
| 29 | $[29, 29, 2w^{2} + w - 4]$ | $-\frac{7}{4}e^{2} + \frac{3}{2}e + 11$ |
| 29 | $[29, 29, -w^{2} + 3w + 1]$ | $-4$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{1}{4}e^{2} + 7$ |
| 41 | $[41, 41, 2w^{2} - 3w - 4]$ | $\phantom{-}\frac{3}{2}e^{2} - e - 12$ |
| 41 | $[41, 41, -3w^{2} + w + 3]$ | $-\frac{5}{4}e^{2} - e + 11$ |
| 43 | $[43, 43, w^{2} + 2w - 5]$ | $\phantom{-}e^{2} - e - 12$ |
| 43 | $[43, 43, 2w^{2} + w - 5]$ | $-\frac{3}{4}e^{2} + 7$ |
| 43 | $[43, 43, 3w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 1$ |
| 71 | $[71, 71, 4w^{2} - 3w - 5]$ | $-\frac{1}{2}e^{2} + e - 6$ |
| 71 | $[71, 71, 3w^{2} - 4w - 5]$ | $\phantom{-}2e^{2} - \frac{5}{2}e - 19$ |
| 71 | $[71, 71, -4w^{2} + w + 5]$ | $\phantom{-}e - 4$ |
| 83 | $[83, 83, w^{2} + w - 7]$ | $-\frac{3}{2}e^{2} + \frac{5}{2}e + 7$ |
| 83 | $[83, 83, w^{2} - 2w - 6]$ | $\phantom{-}\frac{3}{4}e^{2} - e - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $239$ | $[239, 239, 6w^{2} - 5w - 7]$ | $-1$ |