Base field 6.6.1397493.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[53,53,w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 6x^{11} - 3x^{10} - 75x^{9} - 80x^{8} + 276x^{7} + 506x^{6} - 188x^{5} - 811x^{4} - 406x^{3} + 12x^{2} + 30x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $...$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $-\frac{211}{5391}e^{11} - \frac{955}{5391}e^{10} + \frac{2756}{5391}e^{9} + \frac{15953}{5391}e^{8} - \frac{8090}{5391}e^{7} - \frac{92327}{5391}e^{6} - \frac{22216}{5391}e^{5} + \frac{208261}{5391}e^{4} + \frac{117995}{5391}e^{3} - \frac{15208}{599}e^{2} - \frac{30763}{1797}e - \frac{3038}{1797}$ |
| 19 | $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ | $...$ |
| 19 | $[19, 19, w^{2} - w - 1]$ | $...$ |
| 37 | $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ | $...$ |
| 37 | $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ | $...$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ | $...$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $\phantom{-}1$ |
| 64 | $[64, 2, -2]$ | $...$ |
| 71 | $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ | $...$ |
| 71 | $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ | $\phantom{-}\frac{167}{599}e^{11} + \frac{489}{599}e^{10} - \frac{2803}{599}e^{9} - \frac{7505}{599}e^{8} + \frac{17449}{599}e^{7} + \frac{40569}{599}e^{6} - \frac{46910}{599}e^{5} - \frac{91070}{599}e^{4} + \frac{40568}{599}e^{3} + \frac{71121}{599}e^{2} + \frac{13794}{599}e - \frac{3543}{599}$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ | $...$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ | $...$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ | $...$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ | $...$ |
| 89 | $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ | $...$ |
| 89 | $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ | $...$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ | $...$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53,53,w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 2]$ | $-1$ |