Defining parameters
| Level: | \( N \) | = | \( 72 = 2^{3} \cdot 3^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(72))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 50 | 11 | 39 |
| Cusp forms | 2 | 2 | 0 |
| Eisenstein series | 48 | 9 | 39 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)
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 |
|---|---|---|---|---|
| 72.1.b | \(\chi_{72}(19, \cdot)\) | None | 0 | 1 |
| 72.1.e | \(\chi_{72}(17, \cdot)\) | None | 0 | 1 |
| 72.1.g | \(\chi_{72}(55, \cdot)\) | None | 0 | 1 |
| 72.1.h | \(\chi_{72}(53, \cdot)\) | None | 0 | 1 |
| 72.1.j | \(\chi_{72}(5, \cdot)\) | None | 0 | 2 |
| 72.1.k | \(\chi_{72}(7, \cdot)\) | None | 0 | 2 |
| 72.1.m | \(\chi_{72}(41, \cdot)\) | None | 0 | 2 |
| 72.1.p | \(\chi_{72}(43, \cdot)\) | 72.1.p.a | 2 | 2 |