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: | $[53,53,4w^{5} - 14w^{4} - 4w^{3} + 27w^{2} - 4w - 6]$ |
| Dimension: | $29$ |
| 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:
| \(x^{29} - 8x^{28} - 117x^{27} + 1021x^{26} + 5968x^{25} - 57888x^{24} - 174723x^{23} + 1927922x^{22} + 3245372x^{21} - 41975238x^{20} - 39730126x^{19} + 628483297x^{18} + 318752002x^{17} - 6621600439x^{16} - 1544415778x^{15} + 49344280897x^{14} + 2728337822x^{13} - 257667120620x^{12} + 17408462417x^{11} + 920300843934x^{10} - 146578198893x^{9} - 2151874932176x^{8} + 493234650569x^{7} + 3045267144405x^{6} - 826752469995x^{5} - 2230782106970x^{4} + 570550993006x^{3} + 563612691548x^{2} - 29330295157x - 4803664933\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{5} - 4w^{4} + 9w^{2} - w - 3]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{4} - 3w^{3} - 2w^{2} + 5w]$ | $...$ |
| 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 | $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ | $...$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 3]$ | $...$ |
| 53 | $[53, 53, -4w^{5} + 14w^{4} + 4w^{3} - 27w^{2} + 4w + 6]$ | $\phantom{-}1$ |
| 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 |
|---|---|---|
| $53$ | $[53,53,4w^{5} - 14w^{4} - 4w^{3} + 27w^{2} - 4w - 6]$ | $-1$ |