Defining parameters
| Level: | \( N \) | = | \( 207 = 3^{2} \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(3168\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(207))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 186 | 102 | 84 |
| Cusp forms | 10 | 7 | 3 |
| Eisenstein series | 176 | 95 | 81 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(207))\)
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 |
|---|---|---|---|---|
| 207.1.b | \(\chi_{207}(116, \cdot)\) | None | 0 | 1 |
| 207.1.d | \(\chi_{207}(91, \cdot)\) | 207.1.d.a | 1 | 1 |
| 207.1.f | \(\chi_{207}(22, \cdot)\) | 207.1.f.a | 6 | 2 |
| 207.1.h | \(\chi_{207}(47, \cdot)\) | None | 0 | 2 |
| 207.1.j | \(\chi_{207}(10, \cdot)\) | None | 0 | 10 |
| 207.1.l | \(\chi_{207}(8, \cdot)\) | None | 0 | 10 |
| 207.1.n | \(\chi_{207}(2, \cdot)\) | None | 0 | 20 |
| 207.1.p | \(\chi_{207}(7, \cdot)\) | None | 0 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(207))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(207)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)