Base field \(\Q(\zeta_{7})^+\)
Generator \(w\), with minimal polynomial \(x^3 - x^2 - 2 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[71,71,-3 w^2 - w + 6]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $1$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, 2 w^2 - w - 3]$ | $-2$ |
| 8 | $[8, 2, 2]$ | $-1$ |
| 13 | $[13, 13, -w^2 - w + 3]$ | $\phantom{-}4$ |
| 13 | $[13, 13, -w^2 + 2 w + 2]$ | $\phantom{-}4$ |
| 13 | $[13, 13, -2 w^2 + w + 2]$ | $-6$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}8$ |
| 29 | $[29, 29, 3 w^2 - 2 w - 4]$ | $-10$ |
| 29 | $[29, 29, 2 w^2 + w - 4]$ | $-10$ |
| 29 | $[29, 29, -w^2 + 3 w + 1]$ | $\phantom{-}0$ |
| 41 | $[41, 41, w^2 - w - 5]$ | $\phantom{-}2$ |
| 41 | $[41, 41, 2 w^2 - 3 w - 4]$ | $-8$ |
| 41 | $[41, 41, -3 w^2 + w + 3]$ | $\phantom{-}2$ |
| 43 | $[43, 43, w^2 + 2 w - 5]$ | $\phantom{-}4$ |
| 43 | $[43, 43, 2 w^2 + w - 5]$ | $-6$ |
| 43 | $[43, 43, 3 w^2 - 2 w - 3]$ | $\phantom{-}4$ |
| 71 | $[71, 71, 4 w^2 - 3 w - 5]$ | $\phantom{-}2$ |
| 71 | $[71, 71, 3 w^2 - 4 w - 5]$ | $\phantom{-}1$ |
| 71 | $[71, 71, -4 w^2 + w + 5]$ | $-8$ |
| 83 | $[83, 83, w^2 + w - 7]$ | $\phantom{-}4$ |
| 83 | $[83, 83, w^2 - 2 w - 6]$ | $\phantom{-}4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $71$ | $[71,71,-3 w^2 - w + 6]$ | $-1$ |