Base field 6.6.1767625.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[16, 4, w^{5} - 7w^{3} - w^{2} + 10w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 7x^{2} + x + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w + 1]$ | $\phantom{-}0$ |
| 9 | $[9, 3, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{3}{2}w^{2} - 5w + \frac{1}{2}]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$ | $-e + 2$ |
| 16 | $[16, 2, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{5}{2}w^{2} - 3w + \frac{5}{2}]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 7$ |
| 29 | $[29, 29, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 4w^{3} + \frac{5}{2}w^{2} - 6w + \frac{1}{2}]$ | $-\frac{1}{3}e^{2} + \frac{5}{3}e - 4$ |
| 41 | $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{3}{2}w^{2} + 3w + \frac{3}{2}]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{7}{3}e - 6$ |
| 41 | $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 2w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e + 2$ |
| 59 | $[59, 59, -\frac{3}{2}w^{5} + \frac{1}{2}w^{4} + 9w^{3} + \frac{1}{2}w^{2} - 11w - \frac{5}{2}]$ | $-e + 8$ |
| 59 | $[59, 59, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 3w^{3} + \frac{5}{2}w^{2} - 4w - \frac{1}{2}]$ | $-e^{2} + 5e + 6$ |
| 59 | $[59, 59, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 2w^{3} - \frac{1}{2}w^{2} - \frac{3}{2}]$ | $\phantom{-}\frac{5}{3}e^{2} - \frac{19}{3}e - 8$ |
| 59 | $[59, 59, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 11w - \frac{1}{2}]$ | $-\frac{1}{3}e^{2} - \frac{4}{3}e + 8$ |
| 61 | $[61, 61, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{1}{2}w^{2} + 4w + \frac{5}{2}]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e - 2$ |
| 71 | $[71, 71, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 5w^{3} + \frac{5}{2}w^{2} - 11w - \frac{3}{2}]$ | $-\frac{1}{3}e^{2} + \frac{2}{3}e + 4$ |
| 71 | $[71, 71, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 4w^{3} - \frac{5}{2}w^{2} - 7w + \frac{3}{2}]$ | $\phantom{-}e^{2} - 3e - 4$ |
| 79 | $[79, 79, -w^{5} + 6w^{3} + 2w^{2} - 8w - 2]$ | $-e^{2} + 2e + 10$ |
| 79 | $[79, 79, -\frac{3}{2}w^{5} + \frac{3}{2}w^{4} + 9w^{3} - \frac{11}{2}w^{2} - 12w + \frac{3}{2}]$ | $-e^{2} + 3e + 4$ |
| 81 | $[81, 3, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 8w + \frac{3}{2}]$ | $-e^{2} + 5e + 2$ |
| 89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 14w + \frac{7}{2}]$ | $-e^{2} + 4e + 14$ |
| 89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 10w - \frac{1}{2}]$ | $\phantom{-}2e^{2} - 8e - 10$ |
| 89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 15w + \frac{9}{2}]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w + 1]$ | $1$ |