Base field 3.3.1257.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 9\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[15, 15, w^{2} - 6]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 5x^{3} + 3x^{2} - 11x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 3]$ | $-1$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} + w - 5]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $-e^{3} - 3e^{2} + e + 5$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}e^{3} + 3e^{2} - e - 2$ |
| 13 | $[13, 13, -2w + 5]$ | $-e^{3} - 2e^{2} + 4e + 2$ |
| 13 | $[13, 13, -w^{2} - w + 4]$ | $-e^{3} - 4e^{2} + e + 6$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $-e - 4$ |
| 23 | $[23, 23, -w^{2} - w + 7]$ | $-e^{3} - 2e^{2} + 3e + 4$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $\phantom{-}e^{3} + 4e^{2} - e - 10$ |
| 29 | $[29, 29, w^{2} - 5]$ | $\phantom{-}2e^{3} + 6e^{2} - 4e - 10$ |
| 31 | $[31, 31, w^{2} + w - 8]$ | $\phantom{-}e^{3} + 2e^{2} - 6e - 8$ |
| 41 | $[41, 41, w^{2} + w - 11]$ | $\phantom{-}e^{3} + 4e^{2} + 3e - 6$ |
| 47 | $[47, 47, w^{2} + 2w - 1]$ | $\phantom{-}2e^{2} + 6e$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $-e^{3} - 4e^{2} + 3e + 12$ |
| 61 | $[61, 61, -w^{2} + 5w - 7]$ | $-3e^{2} - 2e + 14$ |
| 67 | $[67, 67, 2w^{2} - 13]$ | $-2e^{3} - 6e^{2} + 3e + 4$ |
| 89 | $[89, 89, -2w^{2} + w + 20]$ | $\phantom{-}5e^{3} + 14e^{2} - 11e - 22$ |
| 89 | $[89, 89, 5w^{2} + 8w - 19]$ | $-e^{3} - 6e^{2} - 5e + 6$ |
| 89 | $[89, 89, w^{2} + 2w - 7]$ | $\phantom{-}3e^{3} + 8e^{2} - 9e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 3]$ | $1$ |
| $5$ | $[5, 5, w^{2} + w - 5]$ | $1$ |