Base field 6.6.1528713.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 3w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 12x^{2} + 4x + 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{5} - 4w^{4} + 9w^{2} - w - 3]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{4} - 3w^{3} - 2w^{2} + 5w]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + 2e - 3$ |
| 9 | $[9, 3, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 1]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 3$ |
| 19 | $[19, 19, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 3w + 1]$ | $-1$ |
| 19 | $[19, 19, -w + 2]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{3}{4}e^{2} - 6e + 2$ |
| 37 | $[37, 37, 2w^{5} - 6w^{4} - 5w^{3} + 11w^{2} + 3w - 2]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{7}{2}e - 10$ |
| 37 | $[37, 37, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{7}{4}e^{2} - 6e + 5$ |
| 53 | $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$ | $\phantom{-}2e^{2} - 12$ |
| 53 | $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{5}{2}e - 9$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{13}{2}e$ |
| 53 | $[53, 53, -4w^{5} + 14w^{4} + 4w^{3} - 27w^{2} + 4w + 6]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{5}{2}e$ |
| 71 | $[71, 71, -w^{5} + 2w^{4} + 5w^{3} - 3w^{2} - 3w - 1]$ | $-\frac{1}{2}e^{3} + 3e^{2} + \frac{5}{2}e - 21$ |
| 71 | $[71, 71, 2w^{5} - 8w^{4} + w^{3} + 16w^{2} - 7w - 6]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{11}{4}e^{2} - \frac{1}{2}e + 15$ |
| 73 | $[73, 73, -3w^{5} + 10w^{4} + 5w^{3} - 20w^{2} - 2w + 6]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{5}{2}e - 4$ |
| 73 | $[73, 73, -w^{5} + 3w^{4} + 2w^{3} - 4w^{2} - 2]$ | $-e^{3} + e^{2} + 11e - 1$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{5}{4}e^{3} + \frac{7}{4}e^{2} + \frac{17}{2}e - 7$ |
| 73 | $[73, 73, w^{4} - 2w^{3} - 5w^{2} + 4w + 4]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + 3e - 1$ |
| 89 | $[89, 89, -w^{5} + 3w^{4} + 2w^{3} - 5w^{2} + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - 5e + 9$ |
| 89 | $[89, 89, 3w^{5} - 10w^{4} - 5w^{3} + 21w^{2} - 5]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 6e + 3$ |
| 107 | $[107, 107, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w^{5}+3w^{4}+3w^{3}-7w^{2}-3w+1]$ | $1$ |