Base field 3.3.892.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 10\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w^{2} + w - 9]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 5x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w + 1]$ | $-e^{3} - e^{2} + 5e$ |
| 5 | $[5, 5, -w^{2} - w + 5]$ | $-e^{3} - e^{2} + 4e - 2$ |
| 7 | $[7, 7, w^{2} + w - 9]$ | $-1$ |
| 13 | $[13, 13, -w^{2} - w + 7]$ | $\phantom{-}e^{2} + 3e - 4$ |
| 19 | $[19, 19, w^{2} - w - 1]$ | $\phantom{-}3e^{3} + 5e^{2} - 13e - 3$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $-6$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}2e^{3} + 3e^{2} - 6e - 3$ |
| 31 | $[31, 31, -w^{2} + w + 11]$ | $-e^{2} - 3e + 2$ |
| 43 | $[43, 43, -3w^{2} - w + 21]$ | $-e^{3} - e^{2} + 2e - 6$ |
| 47 | $[47, 47, 2w - 1]$ | $\phantom{-}e^{3} - e^{2} - 7e + 3$ |
| 49 | $[49, 7, 4w^{2} + 2w - 29]$ | $\phantom{-}2e^{3} + e^{2} - 15e$ |
| 61 | $[61, 61, 2w^{2} + 2w - 9]$ | $-2e^{3} - 3e^{2} + 4e + 3$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $\phantom{-}2e^{3} - 17e + 5$ |
| 71 | $[71, 71, -w^{2} - 3w + 7]$ | $-6e^{3} - 9e^{2} + 23e + 6$ |
| 71 | $[71, 71, 2w^{2} + 2w - 13]$ | $\phantom{-}3e^{3} + e^{2} - 14e + 8$ |
| 79 | $[79, 79, w^{2} + 3w - 1]$ | $-e^{3} - 2e^{2} + e - 6$ |
| 79 | $[79, 79, w^{2} + w - 1]$ | $-7e^{3} - 5e^{2} + 35e + 1$ |
| 79 | $[79, 79, -w^{2} - 3w - 1]$ | $-4e^{2} - 2e + 10$ |
| 83 | $[83, 83, w^{2} - w - 7]$ | $-6e^{3} - 6e^{2} + 31e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{2} + w - 9]$ | $1$ |