Base field 6.6.810448.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[27,3,w^{3} - w^{2} - 4w + 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 2x^{2} - 36x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}2$ |
| 25 | $[25, 5, w^{4} - 2w^{3} - 2w^{2} + 3w + 1]$ | $-\frac{1}{4}e^{2} + 7$ |
| 25 | $[25, 5, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - 2w + 2]$ | $\phantom{-}e$ |
| 25 | $[25, 5, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $\phantom{-}\frac{1}{4}e^{2} - e - 5$ |
| 27 | $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}0$ |
| 27 | $[27, 3, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 6w - 4]$ | $-1$ |
| 37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 3w + 2]$ | $-\frac{1}{4}e^{2} - e + 9$ |
| 37 | $[37, 37, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 5w + 5]$ | $-\frac{1}{4}e^{2} + 2e + 7$ |
| 37 | $[37, 37, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} - 2]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 10$ |
| 67 | $[67, 67, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 2e - 10$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 7w - 5]$ | $-\frac{1}{4}e^{2} + 7$ |
| 67 | $[67, 67, -2w^{5} + 6w^{4} + 4w^{3} - 16w^{2} - 3w + 5]$ | $-\frac{1}{2}e^{2} + 14$ |
| 67 | $[67, 67, -2w^{5} + 4w^{4} + 8w^{3} - 12w^{2} - 9w + 6]$ | $\phantom{-}e$ |
| 67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 6w + 4]$ | $\phantom{-}2e$ |
| 67 | $[67, 67, w^{5} - 4w^{4} + 10w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{2} - e - 5$ |
| 107 | $[107, 107, w^{5} - 3w^{4} - w^{3} + 7w^{2} - 3w - 2]$ | $-\frac{1}{4}e^{2} - 2e + 15$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 5]$ | $-\frac{1}{2}e^{2} + 3e + 18$ |
| 107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 13w^{2} + 6w - 4]$ | $\phantom{-}\frac{3}{4}e^{2} - e - 11$ |
| 107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 15w^{2} + 4w - 6]$ | $-e - 6$ |
| 107 | $[107, 107, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $-\frac{1}{4}e^{2} + e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27,3,w^{3} - w^{2} - 4w + 2]$ | $1$ |