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: | $[139,139,-w^{2} + 5w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, 2w^{2} - w - 3]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{2}e + \frac{3}{2}$ |
| 13 | $[13, 13, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{2}e - \frac{3}{2}$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-e - 1$ |
| 13 | $[13, 13, -2w^{2} + w + 2]$ | $-e - 1$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}e - 3$ |
| 29 | $[29, 29, 3w^{2} - 2w - 4]$ | $-2e$ |
| 29 | $[29, 29, 2w^{2} + w - 4]$ | $-\frac{1}{2}e - \frac{1}{2}$ |
| 29 | $[29, 29, -w^{2} + 3w + 1]$ | $\phantom{-}e - 1$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{3}{2}e - \frac{9}{2}$ |
| 41 | $[41, 41, 2w^{2} - 3w - 4]$ | $-e + 4$ |
| 41 | $[41, 41, -3w^{2} + w + 3]$ | $-4$ |
| 43 | $[43, 43, w^{2} + 2w - 5]$ | $\phantom{-}\frac{3}{2}e - \frac{5}{2}$ |
| 43 | $[43, 43, 2w^{2} + w - 5]$ | $-2$ |
| 43 | $[43, 43, 3w^{2} - 2w - 3]$ | $\phantom{-}2e + 5$ |
| 71 | $[71, 71, 4w^{2} - 3w - 5]$ | $-e + 11$ |
| 71 | $[71, 71, 3w^{2} - 4w - 5]$ | $\phantom{-}e - 5$ |
| 71 | $[71, 71, -4w^{2} + w + 5]$ | $-2e - 4$ |
| 83 | $[83, 83, w^{2} + w - 7]$ | $-\frac{3}{2}e - \frac{15}{2}$ |
| 83 | $[83, 83, w^{2} - 2w - 6]$ | $-8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $139$ | $[139,139,-w^{2} + 5w + 1]$ | $-1$ |