Defining parameters
| Level: | \( N \) | = | \( 799 = 17 \cdot 47 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 8 \) | ||
| Sturm bound: | \(52992\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(799))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 781 | 715 | 66 |
| Cusp forms | 45 | 41 | 4 |
| Eisenstein series | 736 | 674 | 62 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 41 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(799))\)
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 |
|---|---|---|---|---|
| 799.1.c | \(\chi_{799}(798, \cdot)\) | 799.1.c.a | 1 | 1 |
| 799.1.c.b | 2 | |||
| 799.1.c.c | 4 | |||
| 799.1.c.d | 4 | |||
| 799.1.d | \(\chi_{799}(375, \cdot)\) | None | 0 | 1 |
| 799.1.e | \(\chi_{799}(140, \cdot)\) | 799.1.e.a | 2 | 2 |
| 799.1.e.b | 8 | |||
| 799.1.h | \(\chi_{799}(93, \cdot)\) | 799.1.h.a | 4 | 4 |
| 799.1.h.b | 16 | |||
| 799.1.i | \(\chi_{799}(48, \cdot)\) | None | 0 | 8 |
| 799.1.l | \(\chi_{799}(35, \cdot)\) | None | 0 | 22 |
| 799.1.m | \(\chi_{799}(33, \cdot)\) | None | 0 | 22 |
| 799.1.p | \(\chi_{799}(13, \cdot)\) | None | 0 | 44 |
| 799.1.q | \(\chi_{799}(15, \cdot)\) | None | 0 | 88 |
| 799.1.t | \(\chi_{799}(3, \cdot)\) | None | 0 | 176 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(799))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(799)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 2}\)