Defining parameters
| Level: | \( N \) | = | \( 208 = 2^{4} \cdot 13 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(2688\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(208))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 181 | 53 | 128 |
| Cusp forms | 13 | 3 | 10 |
| Eisenstein series | 168 | 50 | 118 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(208))\)
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 |
|---|---|---|---|---|
| 208.1.c | \(\chi_{208}(207, \cdot)\) | 208.1.c.a | 1 | 1 |
| 208.1.d | \(\chi_{208}(79, \cdot)\) | None | 0 | 1 |
| 208.1.g | \(\chi_{208}(183, \cdot)\) | None | 0 | 1 |
| 208.1.h | \(\chi_{208}(103, \cdot)\) | None | 0 | 1 |
| 208.1.j | \(\chi_{208}(57, \cdot)\) | None | 0 | 2 |
| 208.1.m | \(\chi_{208}(21, \cdot)\) | None | 0 | 2 |
| 208.1.o | \(\chi_{208}(51, \cdot)\) | None | 0 | 2 |
| 208.1.q | \(\chi_{208}(27, \cdot)\) | None | 0 | 2 |
| 208.1.r | \(\chi_{208}(5, \cdot)\) | None | 0 | 2 |
| 208.1.t | \(\chi_{208}(161, \cdot)\) | None | 0 | 2 |
| 208.1.v | \(\chi_{208}(55, \cdot)\) | None | 0 | 2 |
| 208.1.x | \(\chi_{208}(23, \cdot)\) | None | 0 | 2 |
| 208.1.y | \(\chi_{208}(95, \cdot)\) | 208.1.y.a | 2 | 2 |
| 208.1.bb | \(\chi_{208}(159, \cdot)\) | None | 0 | 2 |
| 208.1.bd | \(\chi_{208}(33, \cdot)\) | None | 0 | 4 |
| 208.1.be | \(\chi_{208}(37, \cdot)\) | None | 0 | 4 |
| 208.1.bg | \(\chi_{208}(3, \cdot)\) | None | 0 | 4 |
| 208.1.bi | \(\chi_{208}(43, \cdot)\) | None | 0 | 4 |
| 208.1.bl | \(\chi_{208}(141, \cdot)\) | None | 0 | 4 |
| 208.1.bn | \(\chi_{208}(41, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(208)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)