Defining parameters
| Level: | \( N \) | = | \( 387 = 3^{2} \cdot 43 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(11088\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(387))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 355 | 192 | 163 |
| Cusp forms | 19 | 7 | 12 |
| Eisenstein series | 336 | 185 | 151 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(387))\)
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 |
|---|---|---|---|---|
| 387.1.b | \(\chi_{387}(343, \cdot)\) | 387.1.b.a | 1 | 1 |
| 387.1.c | \(\chi_{387}(44, \cdot)\) | None | 0 | 1 |
| 387.1.i | \(\chi_{387}(251, \cdot)\) | None | 0 | 2 |
| 387.1.j | \(\chi_{387}(37, \cdot)\) | None | 0 | 2 |
| 387.1.n | \(\chi_{387}(265, \cdot)\) | None | 0 | 2 |
| 387.1.o | \(\chi_{387}(92, \cdot)\) | None | 0 | 2 |
| 387.1.p | \(\chi_{387}(221, \cdot)\) | None | 0 | 2 |
| 387.1.q | \(\chi_{387}(173, \cdot)\) | None | 0 | 2 |
| 387.1.r | \(\chi_{387}(7, \cdot)\) | None | 0 | 2 |
| 387.1.s | \(\chi_{387}(85, \cdot)\) | None | 0 | 2 |
| 387.1.w | \(\chi_{387}(82, \cdot)\) | 387.1.w.a | 6 | 6 |
| 387.1.x | \(\chi_{387}(35, \cdot)\) | None | 0 | 6 |
| 387.1.bd | \(\chi_{387}(11, \cdot)\) | None | 0 | 12 |
| 387.1.be | \(\chi_{387}(23, \cdot)\) | None | 0 | 12 |
| 387.1.bf | \(\chi_{387}(22, \cdot)\) | None | 0 | 12 |
| 387.1.bg | \(\chi_{387}(34, \cdot)\) | None | 0 | 12 |
| 387.1.bh | \(\chi_{387}(106, \cdot)\) | None | 0 | 12 |
| 387.1.bi | \(\chi_{387}(14, \cdot)\) | None | 0 | 12 |
| 387.1.bm | \(\chi_{387}(17, \cdot)\) | None | 0 | 12 |
| 387.1.bn | \(\chi_{387}(19, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(387)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)