Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} + 6]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 2x^{11} - 56x^{10} - 97x^{9} + 1130x^{8} + 1649x^{7} - 9868x^{6} - 11978x^{5} + 35133x^{4} + 38543x^{3} - 38960x^{2} - 47327x - 8797\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $...$ |
| 9 | $[9, 3, -w^{3} + 8w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 25 | $[25, 5, 2w^{2} - 2w - 13]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 9]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 2w + 6]$ | $...$ |
| 29 | $[29, 29, w^{2} - 7]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 2w + 8]$ | $...$ |
| 31 | $[31, 31, -2w^{2} + w + 12]$ | $...$ |
| 31 | $[31, 31, 2w^{2} - 3w - 11]$ | $...$ |
| 41 | $[41, 41, -w]$ | $...$ |
| 41 | $[41, 41, -w + 1]$ | $...$ |
| 49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $...$ |
| 49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $...$ |
| 61 | $[61, 61, 2w^{2} - 3w - 14]$ | $...$ |
| 61 | $[61, 61, 2w^{2} - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + 6]$ | $-1$ |