Defining parameters
| Level: | \( N \) | = | \( 99 = 3^{2} \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(720\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(99))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 82 | 43 | 39 |
| Cusp forms | 2 | 2 | 0 |
| Eisenstein series | 80 | 41 | 39 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)
We only show spaces with odd 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 |
|---|---|---|---|---|
| 99.1.b | \(\chi_{99}(89, \cdot)\) | None | 0 | 1 |
| 99.1.c | \(\chi_{99}(10, \cdot)\) | None | 0 | 1 |
| 99.1.h | \(\chi_{99}(43, \cdot)\) | 99.1.h.a | 2 | 2 |
| 99.1.i | \(\chi_{99}(23, \cdot)\) | None | 0 | 2 |
| 99.1.k | \(\chi_{99}(19, \cdot)\) | None | 0 | 4 |
| 99.1.l | \(\chi_{99}(26, \cdot)\) | None | 0 | 4 |
| 99.1.n | \(\chi_{99}(5, \cdot)\) | None | 0 | 8 |
| 99.1.o | \(\chi_{99}(7, \cdot)\) | None | 0 | 8 |