Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} + w + 1]$ |
| Dimension: | $19$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{19} - 9x^{18} - 17x^{17} + 378x^{16} - 555x^{15} - 5272x^{14} + 16210x^{13} + 23739x^{12} - 140998x^{11} + 37716x^{10} + 474183x^{9} - 423432x^{8} - 679873x^{7} + 794612x^{6} + 497875x^{5} - 568613x^{4} - 212944x^{3} + 142776x^{2} + 30032x - 11984\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $...$ |
| 5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $...$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $...$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $-1$ |
| 23 | $[23, 23, -w^{3} + 4w + 2]$ | $...$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $...$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $...$ |
| 29 | $[29, 29, -w + 3]$ | $...$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $...$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $...$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $...$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $...$ |
| 59 | $[59, 59, w^{2} + w - 4]$ | $...$ |
| 61 | $[61, 61, -2w^{2} + w + 8]$ | $...$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $...$ |
| 79 | $[79, 79, 2w^{2} + w - 6]$ | $...$ |
| 79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + w + 1]$ | $1$ |