Defining parameters
| Level: | \( N \) | = | \( 759 = 3 \cdot 11 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 10 \) | ||
| Sturm bound: | \(42240\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(759))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 934 | 410 | 524 |
| Cusp forms | 54 | 30 | 24 |
| Eisenstein series | 880 | 380 | 500 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 30 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(759))\)
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 |
|---|---|---|---|---|
| 759.1.c | \(\chi_{759}(254, \cdot)\) | None | 0 | 1 |
| 759.1.d | \(\chi_{759}(208, \cdot)\) | None | 0 | 1 |
| 759.1.g | \(\chi_{759}(298, \cdot)\) | None | 0 | 1 |
| 759.1.h | \(\chi_{759}(758, \cdot)\) | 759.1.h.a | 1 | 1 |
| 759.1.h.b | 1 | |||
| 759.1.h.c | 1 | |||
| 759.1.h.d | 1 | |||
| 759.1.h.e | 1 | |||
| 759.1.h.f | 1 | |||
| 759.1.h.g | 2 | |||
| 759.1.h.h | 2 | |||
| 759.1.j | \(\chi_{759}(68, \cdot)\) | None | 0 | 4 |
| 759.1.k | \(\chi_{759}(91, \cdot)\) | None | 0 | 4 |
| 759.1.n | \(\chi_{759}(139, \cdot)\) | None | 0 | 4 |
| 759.1.o | \(\chi_{759}(47, \cdot)\) | None | 0 | 4 |
| 759.1.r | \(\chi_{759}(65, \cdot)\) | 759.1.r.a | 10 | 10 |
| 759.1.r.b | 10 | |||
| 759.1.s | \(\chi_{759}(34, \cdot)\) | None | 0 | 10 |
| 759.1.v | \(\chi_{759}(142, \cdot)\) | None | 0 | 10 |
| 759.1.w | \(\chi_{759}(188, \cdot)\) | None | 0 | 10 |
| 759.1.ba | \(\chi_{759}(26, \cdot)\) | None | 0 | 40 |
| 759.1.bb | \(\chi_{759}(13, \cdot)\) | None | 0 | 40 |
| 759.1.be | \(\chi_{759}(37, \cdot)\) | None | 0 | 40 |
| 759.1.bf | \(\chi_{759}(17, \cdot)\) | None | 0 | 40 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(759))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(759)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(253))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(759))\)\(^{\oplus 1}\)