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: | $[27, 3, 3]$ |
| Dimension: | $31$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $53$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{31} + x^{30} - 101x^{29} - 79x^{28} + 4538x^{27} + 2603x^{26} - 119787x^{25} - 45390x^{24} + 2067107x^{23} + 420031x^{22} - 24564675x^{21} - 1267272x^{20} + 206410333x^{19} - 14637673x^{18} - 1240702836x^{17} + 198180004x^{16} + 5342420987x^{15} - 1126751959x^{14} - 16362856015x^{13} + 3623689631x^{12} + 35066845703x^{11} - 6661380725x^{10} - 51028432564x^{9} + 6003481030x^{8} + 47748627828x^{7} - 498945128x^{6} - 25848334768x^{5} - 3044982208x^{4} + 6407603904x^{3} + 1524159360x^{2} - 386726400x - 110522880\) |
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 | $[27, 3, 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $...$ |
| 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 |
|---|---|---|
| $27$ | $[27, 3, 3]$ | $-1$ |