Base field 3.3.1101.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, w + 1]$ |
| Dimension: | $21$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $39$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{21} - 8x^{20} - 3x^{19} + 177x^{18} - 285x^{17} - 1496x^{16} + 4108x^{15} + 5529x^{14} - 25446x^{13} - 3705x^{12} + 84397x^{11} - 38356x^{10} - 154074x^{9} + 132523x^{8} + 142416x^{7} - 183335x^{6} - 44393x^{5} + 112045x^{4} - 12582x^{3} - 22971x^{2} + 4189x + 1261\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 3]$ | $...$ |
| 3 | $[3, 3, w - 1]$ | $...$ |
| 4 | $[4, 2, w^{2} + w - 7]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $...$ |
| 31 | $[31, 31, -2w^{2} + 19]$ | $...$ |
| 31 | $[31, 31, -w^{2} + 5]$ | $...$ |
| 31 | $[31, 31, -3w + 5]$ | $...$ |
| 41 | $[41, 41, w^{2} + 2w - 7]$ | $...$ |
| 43 | $[43, 43, w^{2} - 11]$ | $...$ |
| 47 | $[47, 47, 3w - 7]$ | $...$ |
| 53 | $[53, 53, -3w^{2} - 6w + 11]$ | $...$ |
| 59 | $[59, 59, 2w - 1]$ | $...$ |
| 67 | $[67, 67, 2w^{2} + w - 19]$ | $...$ |
| 67 | $[67, 67, 3w^{2} + 2w - 25]$ | $...$ |
| 67 | $[67, 67, w - 5]$ | $...$ |
| 73 | $[73, 73, -4w^{2} - 3w + 29]$ | $...$ |
| 73 | $[73, 73, 2w^{2} - w - 11]$ | $...$ |
| 73 | $[73, 73, w^{2} + 2w - 11]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w + 1]$ | $-1$ |