Defining parameters
| Level: | \( N \) | = | \( 104 = 2^{3} \cdot 13 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(672\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(104))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 78 | 24 | 54 |
| Cusp forms | 6 | 2 | 4 |
| Eisenstein series | 72 | 22 | 50 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)
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 |
|---|---|---|---|---|
| 104.1.c | \(\chi_{104}(103, \cdot)\) | None | 0 | 1 |
| 104.1.d | \(\chi_{104}(79, \cdot)\) | None | 0 | 1 |
| 104.1.g | \(\chi_{104}(27, \cdot)\) | None | 0 | 1 |
| 104.1.h | \(\chi_{104}(51, \cdot)\) | 104.1.h.a | 1 | 1 |
| 104.1.h.b | 1 | |||
| 104.1.j | \(\chi_{104}(5, \cdot)\) | None | 0 | 2 |
| 104.1.l | \(\chi_{104}(57, \cdot)\) | None | 0 | 2 |
| 104.1.n | \(\chi_{104}(3, \cdot)\) | None | 0 | 2 |
| 104.1.p | \(\chi_{104}(43, \cdot)\) | None | 0 | 2 |
| 104.1.q | \(\chi_{104}(23, \cdot)\) | None | 0 | 2 |
| 104.1.t | \(\chi_{104}(55, \cdot)\) | None | 0 | 2 |
| 104.1.v | \(\chi_{104}(33, \cdot)\) | None | 0 | 4 |
| 104.1.x | \(\chi_{104}(37, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(104))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(104)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)