Defining parameters
| Level: | \( N \) | = | \( 767 = 13 \cdot 59 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(48720\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(767))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 708 | 636 | 72 |
| Cusp forms | 12 | 10 | 2 |
| Eisenstein series | 696 | 626 | 70 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(767))\)
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 |
|---|---|---|---|---|
| 767.1.c | \(\chi_{767}(235, \cdot)\) | None | 0 | 1 |
| 767.1.d | \(\chi_{767}(766, \cdot)\) | 767.1.d.a | 5 | 1 |
| 767.1.d.b | 5 | |||
| 767.1.f | \(\chi_{767}(60, \cdot)\) | None | 0 | 2 |
| 767.1.h | \(\chi_{767}(530, \cdot)\) | None | 0 | 2 |
| 767.1.j | \(\chi_{767}(412, \cdot)\) | None | 0 | 2 |
| 767.1.l | \(\chi_{767}(119, \cdot)\) | None | 0 | 4 |
| 767.1.n | \(\chi_{767}(38, \cdot)\) | None | 0 | 28 |
| 767.1.o | \(\chi_{767}(14, \cdot)\) | None | 0 | 28 |
| 767.1.s | \(\chi_{767}(5, \cdot)\) | None | 0 | 56 |
| 767.1.t | \(\chi_{767}(42, \cdot)\) | None | 0 | 56 |
| 767.1.v | \(\chi_{767}(10, \cdot)\) | None | 0 | 56 |
| 767.1.w | \(\chi_{767}(7, \cdot)\) | None | 0 | 112 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(767))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(767)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)