Base field 4.4.16609.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[10, 10, w^{3} - w^{2} - 4w + 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 12x^{2} + 11x + 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + w + 4]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w^{2} + w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 4]$ | $\phantom{-}1$ |
| 8 | $[8, 2, w^{3} - w^{2} - 4w + 5]$ | $\phantom{-}e^{3} + e^{2} - 8e - 5$ |
| 17 | $[17, 17, -w^{2} + w + 5]$ | $-e^{3} - 2e^{2} + 9e + 10$ |
| 27 | $[27, 3, -w^{3} + 4w - 2]$ | $-e^{3} + 7e - 4$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}2e^{3} + 3e^{2} - 16e - 14$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $-2e^{3} - 4e^{2} + 15e + 26$ |
| 37 | $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ | $-2e^{3} - 3e^{2} + 14e + 22$ |
| 41 | $[41, 41, w^{3} - w^{2} - 5w + 2]$ | $-e^{3} + 9e + 2$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}2e^{3} + 4e^{2} - 14e - 24$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $-4e^{3} - 8e^{2} + 32e + 46$ |
| 61 | $[61, 61, 2w^{2} - w - 8]$ | $\phantom{-}4e^{3} + 6e^{2} - 30e - 34$ |
| 67 | $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ | $\phantom{-}2e^{3} - 15e$ |
| 73 | $[73, 73, -w^{2} - 2w + 2]$ | $\phantom{-}2e - 2$ |
| 79 | $[79, 79, w^{2} - 2w - 4]$ | $\phantom{-}2e^{3} + 2e^{2} - 17e - 12$ |
| 89 | $[89, 89, w^{2} + w - 5]$ | $-2e^{3} - 4e^{2} + 14e + 22$ |
| 89 | $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ | $-2e^{3} - 4e^{2} + 14e + 22$ |
| 89 | $[89, 89, w^{3} - 5w - 5]$ | $-2e^{3} - 4e^{2} + 14e + 22$ |
| 89 | $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}2e^{2} + 2e - 18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^{2} + w + 4]$ | $-1$ |
| $5$ | $[5, 5, w^{2} - 4]$ | $-1$ |