Spanning Sk(K(16))±
Click on a nonzero nonlift dimension to see how the Fricke eigenspace was spanned.
Except in the two cases where known old forms suffice,
the link reveals Borcherds product(s) that are used to span
that Fricke eigenspace; the Fricke eigenspace is spanned by these Borcherds product(s) and their repeated images under the Hecke operator T(3).
| k |
dim Sk(K(16)) |
Lifts |
Plus Nonlifts |
Minus Nonlifts |
| 1 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 |
| 3 | 0 | 0 | 0 | 0 |
| 4 | 1 | 1 (+) | 0 | 0 |
| 5 | 2 | 2 (−) | 0 | 0 |
| 6 | 4 | 3 (+) | 1 | 0 |
| 7 | 7 | 5 (−) | 0 | 2 |
| 8 | 11 | 6 (+) | 5 | 0 |
| 9 | 16 | 7 (−) |
1 |
8 |
| 10 | 24 | 9 (+) |
13 |
2 |
| 11 | 33 | 10 (−) |
4 |
19 |
| 12 | 45 | 12 (+) |
27 |
6 |
| 13 | 56 | 12 (−) |
10 |
34 |
| 14 | 74 | 14 (+) |
46 |
14 |