Defining parameters
| Level: | \( N \) | = | \( 56 = 2^{3} \cdot 7 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(192\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(56))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 37 | 11 | 26 |
| Cusp forms | 1 | 1 | 0 |
| Eisenstein series | 36 | 10 | 26 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 1 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)
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 |
|---|---|---|---|---|
| 56.1.c | \(\chi_{56}(41, \cdot)\) | None | 0 | 1 |
| 56.1.d | \(\chi_{56}(15, \cdot)\) | None | 0 | 1 |
| 56.1.g | \(\chi_{56}(43, \cdot)\) | None | 0 | 1 |
| 56.1.h | \(\chi_{56}(13, \cdot)\) | 56.1.h.a | 1 | 1 |
| 56.1.j | \(\chi_{56}(5, \cdot)\) | None | 0 | 2 |
| 56.1.k | \(\chi_{56}(11, \cdot)\) | None | 0 | 2 |
| 56.1.n | \(\chi_{56}(23, \cdot)\) | None | 0 | 2 |
| 56.1.o | \(\chi_{56}(17, \cdot)\) | None | 0 | 2 |