Base field 3.3.940.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[10, 10, -w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 2x + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w^{2} + w + 7]$ | $-1$ |
| 5 | $[5, 5, -w^{2} + w + 5]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 6$ |
| 17 | $[17, 17, -w^{2} + 3w + 1]$ | $-2e + 2$ |
| 23 | $[23, 23, -w^{2} + w + 3]$ | $-2e^{2} + 10$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}2e^{2} + 2e - 8$ |
| 29 | $[29, 29, -w^{2} + 3w - 1]$ | $-2e^{3} + 10e - 2$ |
| 37 | $[37, 37, w^{2} + w + 1]$ | $\phantom{-}2e^{3} + 2e^{2} - 12e - 6$ |
| 41 | $[41, 41, w^{2} - w - 9]$ | $-2$ |
| 43 | $[43, 43, -3w^{2} + 3w + 17]$ | $\phantom{-}e^{3} - 3e$ |
| 47 | $[47, 47, 2w^{2} - 2w - 13]$ | $-e^{3} - 4e^{2} + 3e + 20$ |
| 47 | $[47, 47, -2w + 5]$ | $-3e^{3} - 2e^{2} + 13e + 2$ |
| 53 | $[53, 53, 3w^{2} - w - 19]$ | $-e^{3} - 2e^{2} + 7e + 4$ |
| 59 | $[59, 59, 2w - 1]$ | $-2e^{3} - 8e^{2} + 8e + 28$ |
| 67 | $[67, 67, w^{2} + w - 5]$ | $\phantom{-}e^{3} - 5e + 6$ |
| 71 | $[71, 71, -3w^{2} + w + 21]$ | $-2e^{3} - 6e^{2} + 8e + 24$ |
| 79 | $[79, 79, 3w^{2} - w - 23]$ | $\phantom{-}2e^{3} + 2e^{2} - 8e$ |
| 89 | $[89, 89, 2w^{2} - 4w - 7]$ | $-2e^{2} + 20$ |
| 89 | $[89, 89, -2w^{2} - 2w + 5]$ | $-4e^{3} - 6e^{2} + 14e + 22$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 1]$ | $-1$ |
| $5$ | $[5, 5, -w^{2} + w + 7]$ | $1$ |