Base field 6.6.722000.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 7x^{3} + 4x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[59,59,-3w^{5} + w^{4} + 18w^{3} - 9w^{2} - 15w + 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + x^{2} - 9x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{5} + 6w^{3} - w^{2} - 6w]$ | $\phantom{-}e$ |
| 19 | $[19, 19, 3w^{5} - 2w^{4} - 19w^{3} + 14w^{2} + 18w - 9]$ | $-\frac{3}{4}e^{2} - 2e + \frac{7}{4}$ |
| 29 | $[29, 29, -w^{2} - w + 2]$ | $-e^{2} - e + 8$ |
| 29 | $[29, 29, 2w^{5} - w^{4} - 13w^{3} + 7w^{2} + 14w - 3]$ | $\phantom{-}\frac{1}{2}e + \frac{9}{2}$ |
| 29 | $[29, 29, -2w^{5} + w^{4} + 13w^{3} - 8w^{2} - 15w + 6]$ | $-\frac{1}{4}e^{2} - \frac{1}{2}e - \frac{1}{4}$ |
| 49 | $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ | $\phantom{-}\frac{5}{4}e^{2} - \frac{33}{4}$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$ | $-\frac{1}{2}e^{2} - 2e + \frac{21}{2}$ |
| 49 | $[49, 7, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{2} + \frac{1}{2}e + \frac{17}{4}$ |
| 59 | $[59, 59, -3w^{5} + 2w^{4} + 18w^{3} - 15w^{2} - 14w + 7]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{3}{2}$ |
| 59 | $[59, 59, 2w^{5} - 12w^{3} + 3w^{2} + 12w - 3]$ | $-1$ |
| 59 | $[59, 59, -2w^{5} + w^{4} + 12w^{3} - 8w^{2} - 11w + 3]$ | $\phantom{-}\frac{3}{4}e^{2} + \frac{3}{2}e - \frac{5}{4}$ |
| 61 | $[61, 61, -4w^{5} + 2w^{4} + 24w^{3} - 16w^{2} - 19w + 8]$ | $-\frac{1}{2}e^{2} + 2e + \frac{13}{2}$ |
| 61 | $[61, 61, 5w^{5} - 3w^{4} - 31w^{3} + 22w^{2} + 27w - 13]$ | $-\frac{3}{4}e^{2} - e + \frac{51}{4}$ |
| 61 | $[61, 61, 3w^{5} - w^{4} - 18w^{3} + 9w^{2} + 16w - 4]$ | $-\frac{3}{2}e^{2} - \frac{5}{2}e + 9$ |
| 71 | $[71, 71, 2w^{5} - 12w^{3} + 2w^{2} + 11w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 6$ |
| 71 | $[71, 71, 3w^{5} - 2w^{4} - 18w^{3} + 15w^{2} + 13w - 9]$ | $\phantom{-}\frac{1}{2}e^{2} + 3e + \frac{9}{2}$ |
| 71 | $[71, 71, -w^{5} + w^{4} + 6w^{3} - 7w^{2} - 6w + 5]$ | $-2e + 4$ |
| 79 | $[79, 79, -w^{5} + 7w^{3} - w^{2} - 10w]$ | $\phantom{-}\frac{1}{2}e - \frac{15}{2}$ |
| 79 | $[79, 79, 4w^{5} - 2w^{4} - 25w^{3} + 15w^{2} + 23w - 9]$ | $-\frac{3}{2}e^{2} - e + \frac{5}{2}$ |
| 79 | $[79, 79, -w^{5} + 6w^{3} - 2w^{2} - 7w + 4]$ | $-\frac{3}{2}e^{2} + \frac{27}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59,59,-3w^{5} + w^{4} + 18w^{3} - 9w^{2} - 15w + 3]$ | $1$ |