Base field 6.6.1868969.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 8x^{2} + x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ |
| Dimension: | $27$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{27} - 9x^{26} + 224x^{24} - 477x^{23} - 2122x^{22} + 7709x^{21} + 8168x^{20} - 57826x^{19} + 6265x^{18} + 245682x^{17} - 186017x^{16} - 613914x^{15} + 781406x^{14} + 851657x^{13} - 1651056x^{12} - 480404x^{11} + 1930101x^{10} - 207997x^{9} - 1206152x^{8} + 399810x^{7} + 361815x^{6} - 171921x^{5} - 39691x^{4} + 25606x^{3} + 196x^{2} - 1150x + 112\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $...$ |
| 17 | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $...$ |
| 23 | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $...$ |
| 31 | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ | $-1$ |
| 32 | $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ | $...$ |
| 43 | $[43, 43, w^{4} - 5w^{2} + 3]$ | $...$ |
| 47 | $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ | $...$ |
| 49 | $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ | $...$ |
| 53 | $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ | $...$ |
| 59 | $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $...$ |
| 71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ | $...$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $...$ |
| 83 | $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ | $...$ |
| 83 | $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ | $...$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ | $...$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ | $...$ |
| 89 | $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ | $...$ |
| 89 | $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ | $...$ |
| 101 | $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ | $1$ |