Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[29, 29, w^{2} - w - 3]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} + 6x^{21} - 40x^{20} - 274x^{19} + 640x^{18} + 5254x^{17} - 5203x^{16} - 55203x^{15} + 22398x^{14} + 348017x^{13} - 47486x^{12} - 1354376x^{11} + 41109x^{10} + 3214596x^{9} - 51292x^{8} - 4398732x^{7} + 209409x^{6} + 3057829x^{5} - 269033x^{4} - 835411x^{3} + 104769x^{2} + 52272x - 1161\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 7 | $[7, 7, -w + 2]$ | $...$ |
| 7 | $[7, 7, -w + 1]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $...$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $...$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-1$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $...$ |
| 37 | $[37, 37, -w - 4]$ | $...$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $...$ |
| 47 | $[47, 47, w^{2} - 3]$ | $...$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $...$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $...$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $...$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $...$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^{2} - w - 3]$ | $1$ |