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: | $[19, 19, -w^{2} + w + 4]$ |
| Dimension: | $19$ |
| 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:
| \(x^{19} + 4x^{18} - 28x^{17} - 124x^{16} + 293x^{15} + 1544x^{14} - 1313x^{13} - 9888x^{12} + 1176x^{11} + 34430x^{10} + 10155x^{9} - 62850x^{8} - 33716x^{7} + 52804x^{6} + 34509x^{5} - 16680x^{4} - 12284x^{3} + 576x^{2} + 784x + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 3]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 2]$ | $...$ |
| 5 | $[5, 5, w^{2} + w - 5]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 13 | $[13, 13, w + 2]$ | $...$ |
| 13 | $[13, 13, -2w + 5]$ | $...$ |
| 13 | $[13, 13, -w^{2} - w + 4]$ | $...$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{2} - w + 7]$ | $...$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $...$ |
| 29 | $[29, 29, w^{2} - 5]$ | $...$ |
| 31 | $[31, 31, w^{2} + w - 8]$ | $...$ |
| 41 | $[41, 41, w^{2} + w - 11]$ | $...$ |
| 47 | $[47, 47, w^{2} + 2w - 1]$ | $...$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $...$ |
| 61 | $[61, 61, -w^{2} + 5w - 7]$ | $...$ |
| 67 | $[67, 67, 2w^{2} - 13]$ | $...$ |
| 89 | $[89, 89, -2w^{2} + w + 20]$ | $...$ |
| 89 | $[89, 89, 5w^{2} + 8w - 19]$ | $...$ |
| 89 | $[89, 89, w^{2} + 2w - 7]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + w + 4]$ | $-1$ |