Base field 4.4.17428.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 4x + 6\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 9, w^{2} + w - 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - x^{2} - 4x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 2]$ | $-e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{2} + w + 3]$ | $\phantom{-}0$ |
| 27 | $[27, 3, -w^{3} - 2w^{2} + 3w + 5]$ | $-5$ |
| 29 | $[29, 29, w^{3} + w^{2} - 2w - 1]$ | $-e + 4$ |
| 31 | $[31, 31, -w^{2} - w + 1]$ | $\phantom{-}e^{2} - 4e - 7$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 5w + 7]$ | $\phantom{-}e - 6$ |
| 37 | $[37, 37, -w^{3} + 3w + 1]$ | $-2e + 2$ |
| 41 | $[41, 41, -w^{2} + w + 5]$ | $-2e^{2} + 3e$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 4w - 1]$ | $-3e^{2} + e + 11$ |
| 43 | $[43, 43, -2w - 1]$ | $-e^{2} - 2e + 5$ |
| 47 | $[47, 47, w^{2} + w - 5]$ | $-3e^{2} + 6$ |
| 47 | $[47, 47, 2w^{3} - 3w^{2} - 9w + 11]$ | $-4e^{2} + 5e + 7$ |
| 53 | $[53, 53, w^{3} + 2w^{2} - 5w - 5]$ | $\phantom{-}2e^{2} - 3$ |
| 59 | $[59, 59, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}3e^{2} - 7e - 11$ |
| 59 | $[59, 59, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}e^{2} + 4e - 6$ |
| 71 | $[71, 71, 2w^{3} - 4w^{2} - 10w + 19]$ | $\phantom{-}3e^{2} - e - 10$ |
| 71 | $[71, 71, w^{2} + 3w + 1]$ | $\phantom{-}e^{2} - 3e + 2$ |
| 73 | $[73, 73, w^{3} - 5w + 1]$ | $\phantom{-}e^{2} - 14$ |
| 89 | $[89, 89, -4w^{3} + 7w^{2} + 19w - 29]$ | $-2e^{2} - 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{2} + w + 3]$ | $-1$ |