Base field 6.6.485125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 8x^{3} + 2x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 6x^{3} - 9x^{2} + 102x - 139\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $\phantom{-}e^{3} - 2e^{2} - 18e + 37$ |
| 19 | $[19, 19, w^{3} - 3w - 1]$ | $\phantom{-}e - 1$ |
| 29 | $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $-e^{3} + 3e^{2} + 17e - 44$ |
| 29 | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-1$ |
| 31 | $[31, 31, -w^{4} + 4w^{2} + w - 3]$ | $-e^{3} + \frac{5}{2}e^{2} + \frac{35}{2}e - \frac{87}{2}$ |
| 41 | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - 9e + \frac{59}{2}$ |
| 49 | $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ | $\phantom{-}e^{3} - \frac{7}{2}e^{2} - \frac{33}{2}e + \frac{101}{2}$ |
| 59 | $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ | $-\frac{1}{2}e^{2} - \frac{3}{2}e + \frac{13}{2}$ |
| 59 | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $\phantom{-}\frac{3}{2}e^{3} - 3e^{2} - 26e + \frac{107}{2}$ |
| 59 | $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ | $-\frac{1}{2}e^{3} + 7e + \frac{1}{2}$ |
| 61 | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $\phantom{-}e^{3} - 3e^{2} - 17e + 48$ |
| 64 | $[64, 2, -2]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + \frac{17}{2}e - 36$ |
| 71 | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $\phantom{-}e^{2} + 3e - 19$ |
| 79 | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $-e^{2} + 20$ |
| 79 | $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ | $-\frac{3}{2}e^{3} + 4e^{2} + 27e - \frac{145}{2}$ |
| 79 | $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ | $-e^{3} + e^{2} + 17e - 20$ |
| 81 | $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ | $-2e^{3} + 5e^{2} + 33e - 77$ |
| 89 | $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ | $\phantom{-}e^{3} - 4e^{2} - 16e + 61$ |
| 101 | $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ | $-3e^{3} + 7e^{2} + 51e - 118$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $1$ |