Defining parameters
| Level: | \( N \) | = | \( 372 = 2^{2} \cdot 3 \cdot 31 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(7680\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(372))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 336 | 70 | 266 |
| Cusp forms | 36 | 10 | 26 |
| Eisenstein series | 300 | 60 | 240 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(372))\)
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 |
|---|---|---|---|---|
| 372.1.b | \(\chi_{372}(371, \cdot)\) | None | 0 | 1 |
| 372.1.d | \(\chi_{372}(125, \cdot)\) | None | 0 | 1 |
| 372.1.f | \(\chi_{372}(187, \cdot)\) | None | 0 | 1 |
| 372.1.h | \(\chi_{372}(61, \cdot)\) | None | 0 | 1 |
| 372.1.k | \(\chi_{372}(37, \cdot)\) | None | 0 | 2 |
| 372.1.m | \(\chi_{372}(67, \cdot)\) | None | 0 | 2 |
| 372.1.o | \(\chi_{372}(5, \cdot)\) | 372.1.o.a | 2 | 2 |
| 372.1.q | \(\chi_{372}(119, \cdot)\) | None | 0 | 2 |
| 372.1.s | \(\chi_{372}(101, \cdot)\) | None | 0 | 4 |
| 372.1.u | \(\chi_{372}(23, \cdot)\) | None | 0 | 4 |
| 372.1.v | \(\chi_{372}(85, \cdot)\) | None | 0 | 4 |
| 372.1.x | \(\chi_{372}(163, \cdot)\) | None | 0 | 4 |
| 372.1.z | \(\chi_{372}(7, \cdot)\) | None | 0 | 8 |
| 372.1.bb | \(\chi_{372}(13, \cdot)\) | None | 0 | 8 |
| 372.1.bc | \(\chi_{372}(11, \cdot)\) | None | 0 | 8 |
| 372.1.be | \(\chi_{372}(41, \cdot)\) | 372.1.be.a | 8 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(372))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(372)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 2}\)