Defining parameters
| Level: | \( N \) | = | \( 93 = 3 \cdot 31 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(640\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(93))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 66 | 32 | 34 |
| Cusp forms | 6 | 4 | 2 |
| Eisenstein series | 60 | 28 | 32 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(93))\)
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 the newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 93.1.b | \(\chi_{93}(32, \cdot)\) | None | 0 | 1 |
| 93.1.d | \(\chi_{93}(61, \cdot)\) | None | 0 | 1 |
| 93.1.h | \(\chi_{93}(5, \cdot)\) | None | 0 | 2 |
| 93.1.i | \(\chi_{93}(37, \cdot)\) | None | 0 | 2 |
| 93.1.j | \(\chi_{93}(46, \cdot)\) | None | 0 | 4 |
| 93.1.l | \(\chi_{93}(2, \cdot)\) | 93.1.l.a | 4 | 4 |
| 93.1.n | \(\chi_{93}(13, \cdot)\) | None | 0 | 8 |
| 93.1.o | \(\chi_{93}(14, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(93))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(93)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)