Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} + 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} + x^{2} - 6x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $-e^{2} - 2e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e^{3} + 4e^{2} + 2e - 3$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}e^{3} + 2e^{2} - 2e - 1$ |
| 7 | $[7, 7, -w + 1]$ | $-e^{2} - e + 3$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{3} + e^{2} - 3e + 3$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-1$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-e^{3} + 2e^{2} + 10e - 7$ |
| 27 | $[27, 3, 3]$ | $-2e$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-2e^{3} - 11e^{2} - 8e + 11$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $-e^{3} - e^{2} + e - 6$ |
| 37 | $[37, 37, -w - 4]$ | $-e^{3} - 7e^{2} - 8e + 5$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-4e^{3} - 13e^{2} - e + 7$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}e^{3} + 5e^{2} + 5e - 12$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}e^{3} - 9e - 2$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-3e^{3} - 9e^{2} + 3e + 14$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $\phantom{-}4e^{3} + 13e^{2} + 3e - 9$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $\phantom{-}3e^{3} + 12e^{2} + 4e - 13$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $\phantom{-}e^{3} + 4e^{2} - 5e - 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + 5]$ | $1$ |