Defining parameters
| Level: | \( N \) | = | \( 216 = 2^{3} \cdot 3^{3} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(2592\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(216))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 196 | 42 | 154 |
| Cusp forms | 16 | 10 | 6 |
| Eisenstein series | 180 | 32 | 148 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)
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 |
|---|---|---|---|---|
| 216.1.b | \(\chi_{216}(163, \cdot)\) | None | 0 | 1 |
| 216.1.e | \(\chi_{216}(161, \cdot)\) | None | 0 | 1 |
| 216.1.g | \(\chi_{216}(55, \cdot)\) | None | 0 | 1 |
| 216.1.h | \(\chi_{216}(53, \cdot)\) | 216.1.h.a | 1 | 1 |
| 216.1.h.b | 1 | |||
| 216.1.j | \(\chi_{216}(125, \cdot)\) | None | 0 | 2 |
| 216.1.k | \(\chi_{216}(127, \cdot)\) | None | 0 | 2 |
| 216.1.m | \(\chi_{216}(17, \cdot)\) | None | 0 | 2 |
| 216.1.p | \(\chi_{216}(19, \cdot)\) | 216.1.p.a | 2 | 2 |
| 216.1.r | \(\chi_{216}(43, \cdot)\) | 216.1.r.a | 6 | 6 |
| 216.1.s | \(\chi_{216}(7, \cdot)\) | None | 0 | 6 |
| 216.1.u | \(\chi_{216}(41, \cdot)\) | None | 0 | 6 |
| 216.1.x | \(\chi_{216}(5, \cdot)\) | None | 0 | 6 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(216))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(216)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)