Defining parameters
| Level: | \( N \) | = | \( 111 = 3 \cdot 37 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(912\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(111))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 79 | 41 | 38 |
| Cusp forms | 7 | 7 | 0 |
| Eisenstein series | 72 | 34 | 38 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)
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 |
|---|---|---|---|---|
| 111.1.b | \(\chi_{111}(38, \cdot)\) | None | 0 | 1 |
| 111.1.d | \(\chi_{111}(110, \cdot)\) | 111.1.d.a | 1 | 1 |
| 111.1.d.b | 2 | |||
| 111.1.f | \(\chi_{111}(31, \cdot)\) | None | 0 | 2 |
| 111.1.h | \(\chi_{111}(11, \cdot)\) | 111.1.h.a | 2 | 2 |
| 111.1.i | \(\chi_{111}(26, \cdot)\) | 111.1.i.a | 2 | 2 |
| 111.1.l | \(\chi_{111}(82, \cdot)\) | None | 0 | 4 |
| 111.1.n | \(\chi_{111}(41, \cdot)\) | None | 0 | 6 |
| 111.1.p | \(\chi_{111}(44, \cdot)\) | None | 0 | 6 |
| 111.1.r | \(\chi_{111}(13, \cdot)\) | None | 0 | 12 |