Base field 3.3.1524.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, w^{2} - 3w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 2x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 3w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{2} - w + 3]$ | $-1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, 2w^{2} - 6w - 1]$ | $-e^{2} + 6$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}e^{3} - 6e$ |
| 17 | $[17, 17, -w^{2} + 4w - 2]$ | $-2e^{2} + 8$ |
| 19 | $[19, 19, w^{2} - 6]$ | $\phantom{-}e^{2} - 2$ |
| 19 | $[19, 19, -w^{2} - 3w - 1]$ | $-e^{3} + 6e - 2$ |
| 19 | $[19, 19, 3w^{2} - 9w - 1]$ | $\phantom{-}e^{2} + 2e - 4$ |
| 41 | $[41, 41, w^{2} - 8]$ | $\phantom{-}2e + 6$ |
| 43 | $[43, 43, -2w^{2} - 3w + 4]$ | $\phantom{-}e^{3} - 4e + 2$ |
| 47 | $[47, 47, -2w - 3]$ | $\phantom{-}e^{3} - 10e + 4$ |
| 49 | $[49, 7, -9w^{2} + 29w - 3]$ | $\phantom{-}e^{3} + e^{2} - 6e - 2$ |
| 67 | $[67, 67, 2w - 3]$ | $\phantom{-}e^{2} + 2e - 4$ |
| 71 | $[71, 71, 4w^{2} - 14w + 5]$ | $-2e^{3} - 2e^{2} + 12e + 8$ |
| 79 | $[79, 79, w^{2} - 3w - 3]$ | $\phantom{-}3e^{3} + 4e^{2} - 18e - 6$ |
| 79 | $[79, 79, -w^{2} + 5w - 5]$ | $\phantom{-}2e^{2} + 2e - 12$ |
| 79 | $[79, 79, 6w^{2} - 3w - 38]$ | $-e^{3} - 4e^{2} + 4e + 14$ |
| 97 | $[97, 97, 3w^{2} - 10w]$ | $\phantom{-}2e^{3} - e^{2} - 8e + 14$ |
| 103 | $[103, 103, 3w^{2} - 4w - 24]$ | $-4e^{3} - 3e^{2} + 22e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{2} - w + 3]$ | $1$ |
| $3$ | $[3, 3, w + 2]$ | $-1$ |