Base field 3.3.1489.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w + 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 3x^{2} - x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{2} - 3e$ |
| 13 | $[13, 13, w^{2} - 3w - 5]$ | $\phantom{-}e^{2} - 3e - 1$ |
| 17 | $[17, 17, w - 1]$ | $\phantom{-}e - 4$ |
| 19 | $[19, 19, -w^{2} + 2w + 6]$ | $\phantom{-}2e^{2} - e - 8$ |
| 19 | $[19, 19, -w^{2} + 2w + 10]$ | $-2e^{2} + 3e + 1$ |
| 19 | $[19, 19, -w + 3]$ | $-1$ |
| 23 | $[23, 23, w - 2]$ | $-e^{2} + e + 1$ |
| 27 | $[27, 3, 3]$ | $-e^{2} + 6$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $-e^{2} + 3e + 3$ |
| 31 | $[31, 31, w^{2} - 3w - 6]$ | $-3e^{2} + 4e + 8$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}e - 3$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $-2e^{2} + 5e + 2$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}5e^{2} - 7e - 11$ |
| 43 | $[43, 43, w^{2} - 3w - 10]$ | $-2e^{2} + 2e + 4$ |
| 47 | $[47, 47, -w - 4]$ | $-5e^{2} + 11e + 7$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $-e^{2} + 2e + 11$ |
| 47 | $[47, 47, -2w^{2} + 3w + 17]$ | $\phantom{-}2e^{2} - 5e - 9$ |
| 49 | $[49, 7, w^{2} - w - 10]$ | $-2e - 2$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-e^{2} - 2e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w + 3]$ | $1$ |