Defining parameters
| Level: | \( N \) | = | \( 309 = 3 \cdot 103 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(7072\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(309))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 228 | 120 | 108 |
| Cusp forms | 24 | 20 | 4 |
| Eisenstein series | 204 | 100 | 104 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 16 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(309))\)
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 |
|---|---|---|---|---|
| 309.1.b | \(\chi_{309}(104, \cdot)\) | None | 0 | 1 |
| 309.1.d | \(\chi_{309}(205, \cdot)\) | None | 0 | 1 |
| 309.1.f | \(\chi_{309}(160, \cdot)\) | None | 0 | 2 |
| 309.1.h | \(\chi_{309}(56, \cdot)\) | 309.1.h.a | 4 | 2 |
| 309.1.j | \(\chi_{309}(10, \cdot)\) | None | 0 | 16 |
| 309.1.l | \(\chi_{309}(8, \cdot)\) | 309.1.l.a | 16 | 16 |
| 309.1.n | \(\chi_{309}(2, \cdot)\) | None | 0 | 32 |
| 309.1.p | \(\chi_{309}(40, \cdot)\) | None | 0 | 32 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(309))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(309)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(309))\)\(^{\oplus 1}\)