Base field 6.6.1528713.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ |
| Dimension: | $27$ |
| 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:
| \(x^{27} - 12x^{26} - 42x^{25} + 1038x^{24} - 1330x^{23} - 33900x^{22} + 113218x^{21} + 499498x^{20} - 2769474x^{19} - 2402795x^{18} + 33048720x^{17} - 20844377x^{16} - 203796309x^{15} + 321240150x^{14} + 591004684x^{13} - 1546912943x^{12} - 509140590x^{11} + 3333139733x^{10} - 623072583x^{9} - 3551713976x^{8} + 1327567951x^{7} + 1858479320x^{6} - 744214000x^{5} - 373949697x^{4} + 148183551x^{3} + 4425840x^{2} - 3457269x + 187353\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{5} - 4w^{4} + 9w^{2} - w - 3]$ | $...$ |
| 8 | $[8, 2, w^{4} - 3w^{3} - 2w^{2} + 5w]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 3w + 1]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 37 | $[37, 37, 2w^{5} - 6w^{4} - 5w^{3} + 11w^{2} + 3w - 2]$ | $...$ |
| 37 | $[37, 37, -w^{3} + 3w^{2} + w - 3]$ | $...$ |
| 53 | $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$ | $...$ |
| 53 | $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ | $\phantom{-}1$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 3]$ | $...$ |
| 53 | $[53, 53, -4w^{5} + 14w^{4} + 4w^{3} - 27w^{2} + 4w + 6]$ | $...$ |
| 71 | $[71, 71, -w^{5} + 2w^{4} + 5w^{3} - 3w^{2} - 3w - 1]$ | $...$ |
| 71 | $[71, 71, 2w^{5} - 8w^{4} + w^{3} + 16w^{2} - 7w - 6]$ | $...$ |
| 73 | $[73, 73, -3w^{5} + 10w^{4} + 5w^{3} - 20w^{2} - 2w + 6]$ | $...$ |
| 73 | $[73, 73, -w^{5} + 3w^{4} + 2w^{3} - 4w^{2} - 2]$ | $...$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 2]$ | $...$ |
| 73 | $[73, 73, w^{4} - 2w^{3} - 5w^{2} + 4w + 4]$ | $...$ |
| 89 | $[89, 89, -w^{5} + 3w^{4} + 2w^{3} - 5w^{2} + 3]$ | $...$ |
| 89 | $[89, 89, 3w^{5} - 10w^{4} - 5w^{3} + 21w^{2} - 5]$ | $...$ |
| 107 | $[107, 107, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53,53,2w^{5}-7w^{4}-2w^{3}+14w^{2}-2w-5]$ | $-1$ |