Defining parameters
| Level: | \( N \) | = | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(8640\) | ||
| Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(380))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 379 | 112 | 267 |
| Cusp forms | 19 | 8 | 11 |
| Eisenstein series | 360 | 104 | 256 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(380))\)
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 |
|---|---|---|---|---|
| 380.1.b | \(\chi_{380}(191, \cdot)\) | None | 0 | 1 |
| 380.1.e | \(\chi_{380}(341, \cdot)\) | None | 0 | 1 |
| 380.1.g | \(\chi_{380}(189, \cdot)\) | 380.1.g.a | 2 | 1 |
| 380.1.h | \(\chi_{380}(39, \cdot)\) | None | 0 | 1 |
| 380.1.j | \(\chi_{380}(227, \cdot)\) | None | 0 | 2 |
| 380.1.m | \(\chi_{380}(77, \cdot)\) | None | 0 | 2 |
| 380.1.o | \(\chi_{380}(69, \cdot)\) | 380.1.o.a | 2 | 2 |
| 380.1.p | \(\chi_{380}(159, \cdot)\) | None | 0 | 2 |
| 380.1.q | \(\chi_{380}(11, \cdot)\) | None | 0 | 2 |
| 380.1.t | \(\chi_{380}(141, \cdot)\) | None | 0 | 2 |
| 380.1.w | \(\chi_{380}(27, \cdot)\) | None | 0 | 4 |
| 380.1.x | \(\chi_{380}(197, \cdot)\) | 380.1.x.a | 4 | 4 |
| 380.1.z | \(\chi_{380}(21, \cdot)\) | None | 0 | 6 |
| 380.1.ba | \(\chi_{380}(99, \cdot)\) | None | 0 | 6 |
| 380.1.bc | \(\chi_{380}(29, \cdot)\) | None | 0 | 6 |
| 380.1.bf | \(\chi_{380}(111, \cdot)\) | None | 0 | 6 |
| 380.1.bg | \(\chi_{380}(17, \cdot)\) | None | 0 | 12 |
| 380.1.bi | \(\chi_{380}(3, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(380))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(380)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 3}\)