Defining parameters
| Level: | \( N \) | = | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(4800\) | ||
| Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(300))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 296 | 48 | 248 |
| Cusp forms | 16 | 8 | 8 |
| Eisenstein series | 280 | 40 | 240 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)
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 |
|---|---|---|---|---|
| 300.1.b | \(\chi_{300}(149, \cdot)\) | 300.1.b.a | 2 | 1 |
| 300.1.c | \(\chi_{300}(151, \cdot)\) | None | 0 | 1 |
| 300.1.f | \(\chi_{300}(199, \cdot)\) | None | 0 | 1 |
| 300.1.g | \(\chi_{300}(101, \cdot)\) | 300.1.g.a | 1 | 1 |
| 300.1.g.b | 1 | |||
| 300.1.k | \(\chi_{300}(157, \cdot)\) | None | 0 | 2 |
| 300.1.l | \(\chi_{300}(107, \cdot)\) | 300.1.l.a | 4 | 2 |
| 300.1.p | \(\chi_{300}(31, \cdot)\) | None | 0 | 4 |
| 300.1.q | \(\chi_{300}(29, \cdot)\) | None | 0 | 4 |
| 300.1.s | \(\chi_{300}(41, \cdot)\) | None | 0 | 4 |
| 300.1.t | \(\chi_{300}(19, \cdot)\) | None | 0 | 4 |
| 300.1.u | \(\chi_{300}(23, \cdot)\) | None | 0 | 8 |
| 300.1.v | \(\chi_{300}(13, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(300)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)