Defining parameters
| Level: | \( N \) | = | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(4224\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(276))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 232 | 50 | 182 |
| Cusp forms | 12 | 6 | 6 |
| Eisenstein series | 220 | 44 | 176 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(276))\)
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 |
|---|---|---|---|---|
| 276.1.b | \(\chi_{276}(229, \cdot)\) | None | 0 | 1 |
| 276.1.d | \(\chi_{276}(185, \cdot)\) | None | 0 | 1 |
| 276.1.f | \(\chi_{276}(139, \cdot)\) | None | 0 | 1 |
| 276.1.h | \(\chi_{276}(275, \cdot)\) | 276.1.h.a | 1 | 1 |
| 276.1.h.b | 1 | |||
| 276.1.h.c | 2 | |||
| 276.1.h.d | 2 | |||
| 276.1.j | \(\chi_{276}(11, \cdot)\) | None | 0 | 10 |
| 276.1.l | \(\chi_{276}(31, \cdot)\) | None | 0 | 10 |
| 276.1.n | \(\chi_{276}(29, \cdot)\) | None | 0 | 10 |
| 276.1.p | \(\chi_{276}(37, \cdot)\) | None | 0 | 10 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(276))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(276)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)