Defining parameters
| Level: | \( N \) | = | \( 99 = 3^{2} \cdot 11 \) |
| Weight: | \( k \) | = | \( 6 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Newform subspaces: | \( 21 \) | ||
| Sturm bound: | \(4320\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(99))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1880 | 1442 | 438 |
| Cusp forms | 1720 | 1362 | 358 |
| Eisenstein series | 160 | 80 | 80 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 99.6.a | \(\chi_{99}(1, \cdot)\) | 99.6.a.a | 1 | 1 |
| 99.6.a.b | 1 | |||
| 99.6.a.c | 1 | |||
| 99.6.a.d | 2 | |||
| 99.6.a.e | 2 | |||
| 99.6.a.f | 2 | |||
| 99.6.a.g | 3 | |||
| 99.6.a.h | 5 | |||
| 99.6.a.i | 5 | |||
| 99.6.d | \(\chi_{99}(98, \cdot)\) | 99.6.d.a | 20 | 1 |
| 99.6.e | \(\chi_{99}(34, \cdot)\) | 99.6.e.a | 46 | 2 |
| 99.6.e.b | 54 | |||
| 99.6.f | \(\chi_{99}(37, \cdot)\) | 99.6.f.a | 16 | 4 |
| 99.6.f.b | 20 | |||
| 99.6.f.c | 20 | |||
| 99.6.f.d | 40 | |||
| 99.6.g | \(\chi_{99}(32, \cdot)\) | 99.6.g.a | 4 | 2 |
| 99.6.g.b | 112 | |||
| 99.6.j | \(\chi_{99}(8, \cdot)\) | 99.6.j.a | 80 | 4 |
| 99.6.m | \(\chi_{99}(4, \cdot)\) | 99.6.m.a | 464 | 8 |
| 99.6.p | \(\chi_{99}(2, \cdot)\) | 99.6.p.a | 464 | 8 |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)