Defining parameters
| Level: | \( N \) | = | \( 112 = 2^{4} \cdot 7 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(768\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(112))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 88 | 25 | 63 |
| Cusp forms | 4 | 2 | 2 |
| Eisenstein series | 84 | 23 | 61 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)
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 |
|---|---|---|---|---|
| 112.1.c | \(\chi_{112}(97, \cdot)\) | None | 0 | 1 |
| 112.1.d | \(\chi_{112}(15, \cdot)\) | None | 0 | 1 |
| 112.1.g | \(\chi_{112}(71, \cdot)\) | None | 0 | 1 |
| 112.1.h | \(\chi_{112}(41, \cdot)\) | None | 0 | 1 |
| 112.1.k | \(\chi_{112}(43, \cdot)\) | None | 0 | 2 |
| 112.1.l | \(\chi_{112}(13, \cdot)\) | 112.1.l.a | 2 | 2 |
| 112.1.n | \(\chi_{112}(73, \cdot)\) | None | 0 | 2 |
| 112.1.o | \(\chi_{112}(23, \cdot)\) | None | 0 | 2 |
| 112.1.r | \(\chi_{112}(79, \cdot)\) | None | 0 | 2 |
| 112.1.s | \(\chi_{112}(17, \cdot)\) | None | 0 | 2 |
| 112.1.u | \(\chi_{112}(11, \cdot)\) | None | 0 | 4 |
| 112.1.x | \(\chi_{112}(5, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)