Base field 4.4.10889.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[7, 7, -w + 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - x^{2} - 4x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $-1$ |
| 8 | $[8, 2, -w^{3} + 5w + 3]$ | $\phantom{-}e^{2} - 2e - 2$ |
| 11 | $[11, 11, w^{3} - w^{2} - 5w + 4]$ | $\phantom{-}e^{2} - e - 2$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e + 1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e^{2} - 7$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $-e^{2} + e + 8$ |
| 25 | $[25, 5, -w^{2} + 2]$ | $\phantom{-}4e^{2} - 3e - 9$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $\phantom{-}e + 3$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $-2$ |
| 37 | $[37, 37, 4w^{3} - 2w^{2} - 21w - 4]$ | $-2e^{2} + 2e + 2$ |
| 43 | $[43, 43, 4w^{3} - 2w^{2} - 20w - 3]$ | $-2e^{2} - e + 9$ |
| 47 | $[47, 47, -w^{3} + 6w]$ | $-2e^{2} - e + 13$ |
| 53 | $[53, 53, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}e^{2} + 2e - 9$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{2} + 3e - 8$ |
| 83 | $[83, 83, 2w^{3} - w^{2} - 10w - 4]$ | $\phantom{-}5e^{2} - e - 14$ |
| 89 | $[89, 89, w^{3} - 2w^{2} - 4w + 2]$ | $-6e^{2} + 16$ |
| 89 | $[89, 89, 2w - 3]$ | $\phantom{-}10$ |
| 101 | $[101, 101, 6w^{3} - 3w^{2} - 31w - 5]$ | $-e^{2} + 6e - 3$ |
| 107 | $[107, 107, -w^{3} + w^{2} + 4w - 5]$ | $\phantom{-}e^{2} - 8e - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w + 2]$ | $1$ |