Base field 3.3.756.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} - w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - x^{2} - 5x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{2}e^{2} + e + \frac{3}{2}$ |
| 7 | $[7, 7, -w + 3]$ | $-\frac{1}{2}e^{2} - e + \frac{7}{2}$ |
| 7 | $[7, 7, w - 1]$ | $-\frac{1}{2}e^{2} + e + \frac{5}{2}$ |
| 11 | $[11, 11, -w - 3]$ | $-\frac{1}{2}e^{2} + e + \frac{11}{2}$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $-e^{2} + 1$ |
| 19 | $[19, 19, -w^{2} - w + 1]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{1}{2}$ |
| 29 | $[29, 29, 2w + 3]$ | $\phantom{-}\frac{1}{2}e^{2} + 2e + \frac{3}{2}$ |
| 31 | $[31, 31, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{5}{2}e^{2} - 2e - \frac{15}{2}$ |
| 53 | $[53, 53, -w^{2} - 1]$ | $\phantom{-}2e^{2} - 2e - 3$ |
| 61 | $[61, 61, 2w - 3]$ | $\phantom{-}e^{2} + e - 10$ |
| 67 | $[67, 67, w^{2} - 2w - 5]$ | $\phantom{-}e^{2} + 3e - 4$ |
| 67 | $[67, 67, -w^{2} + w + 9]$ | $-\frac{1}{2}e^{2} - 2e + \frac{3}{2}$ |
| 67 | $[67, 67, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{2}e^{2} - e + \frac{21}{2}$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $-\frac{3}{2}e^{2} - 4e + \frac{13}{2}$ |
| 73 | $[73, 73, -2w^{2} + 3w + 7]$ | $-2e^{2} + 4e + 1$ |
| 89 | $[89, 89, w^{2} - 2w - 7]$ | $-3e + 2$ |
| 89 | $[89, 89, -2w^{2} + 1]$ | $-\frac{5}{2}e^{2} - 2e + \frac{13}{2}$ |
| 89 | $[89, 89, -3w^{2} + 19]$ | $-e^{2} + e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} - w + 1]$ | $-1$ |