Defining parameters
| Level: | \( N \) | = | \( 1012 = 2^{2} \cdot 11 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(63360\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1012))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1158 | 400 | 758 |
| Cusp forms | 58 | 20 | 38 |
| Eisenstein series | 1100 | 380 | 720 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 20 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1012))\)
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 |
|---|---|---|---|---|
| 1012.1.b | \(\chi_{1012}(1011, \cdot)\) | None | 0 | 1 |
| 1012.1.d | \(\chi_{1012}(507, \cdot)\) | None | 0 | 1 |
| 1012.1.f | \(\chi_{1012}(45, \cdot)\) | None | 0 | 1 |
| 1012.1.h | \(\chi_{1012}(461, \cdot)\) | None | 0 | 1 |
| 1012.1.j | \(\chi_{1012}(277, \cdot)\) | None | 0 | 4 |
| 1012.1.l | \(\chi_{1012}(137, \cdot)\) | None | 0 | 4 |
| 1012.1.n | \(\chi_{1012}(47, \cdot)\) | None | 0 | 4 |
| 1012.1.p | \(\chi_{1012}(183, \cdot)\) | None | 0 | 4 |
| 1012.1.r | \(\chi_{1012}(197, \cdot)\) | 1012.1.r.a | 20 | 10 |
| 1012.1.t | \(\chi_{1012}(89, \cdot)\) | None | 0 | 10 |
| 1012.1.v | \(\chi_{1012}(243, \cdot)\) | None | 0 | 10 |
| 1012.1.x | \(\chi_{1012}(43, \cdot)\) | None | 0 | 10 |
| 1012.1.z | \(\chi_{1012}(7, \cdot)\) | None | 0 | 40 |
| 1012.1.bb | \(\chi_{1012}(3, \cdot)\) | None | 0 | 40 |
| 1012.1.bd | \(\chi_{1012}(5, \cdot)\) | None | 0 | 40 |
| 1012.1.bf | \(\chi_{1012}(13, \cdot)\) | None | 0 | 40 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1012))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1012)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(253))\)\(^{\oplus 3}\)