Base field 3.3.257.1
Generator \(w\), with minimal polynomial \(x^3 - x^2 - 4 x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[49, 49, w^2 + w + 1]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-3$ |
| 5 | $[5, 5, w + 1]$ | $-1$ |
| 7 | $[7, 7, -w^2 + 2]$ | $\phantom{-}0$ |
| 8 | $[8, 2, 2]$ | $-5$ |
| 9 | $[9, 3, -w^2 + w + 4]$ | $-4$ |
| 19 | $[19, 19, w^2 + w - 4]$ | $-1$ |
| 25 | $[25, 5, -w^2 + 2 w + 2]$ | $-2$ |
| 37 | $[37, 37, 2 w + 1]$ | $\phantom{-}10$ |
| 41 | $[41, 41, -2 w^2 - w + 7]$ | $\phantom{-}0$ |
| 43 | $[43, 43, -2 w^2 + 5]$ | $\phantom{-}2$ |
| 47 | $[47, 47, 3 w - 4]$ | $-1$ |
| 49 | $[49, 7, 2 w^2 - w - 5]$ | $-6$ |
| 53 | $[53, 53, -2 w^2 + 2 w + 7]$ | $-2$ |
| 61 | $[61, 61, -w^2 - 3 w + 4]$ | $-8$ |
| 61 | $[61, 61, 3 w^2 - w - 10]$ | $-1$ |
| 61 | $[61, 61, w^2 - 2 w - 4]$ | $-8$ |
| 67 | $[67, 67, 2 w^2 - w - 4]$ | $-2$ |
| 67 | $[67, 67, 2 w^2 - w - 2]$ | $\phantom{-}12$ |
| 67 | $[67, 67, w^2 + 2 w - 5]$ | $-9$ |
| 71 | $[71, 71, -2 w^2 - w + 10]$ | $\phantom{-}9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^2 + 2]$ | $-1$ |