Defining parameters
| Level: | \( N \) | = | \( 2864 = 2^{4} \cdot 179 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(512640\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2864))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2708 | 808 | 1900 |
| Cusp forms | 216 | 11 | 205 |
| Eisenstein series | 2492 | 797 | 1695 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 7 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2864))\)
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 |
|---|---|---|---|---|
| 2864.1.b | \(\chi_{2864}(2505, \cdot)\) | None | 0 | 1 |
| 2864.1.d | \(\chi_{2864}(1791, \cdot)\) | None | 0 | 1 |
| 2864.1.f | \(\chi_{2864}(359, \cdot)\) | None | 0 | 1 |
| 2864.1.h | \(\chi_{2864}(1073, \cdot)\) | 2864.1.h.a | 1 | 1 |
| 2864.1.h.b | 2 | |||
| 2864.1.h.c | 4 | |||
| 2864.1.k | \(\chi_{2864}(1075, \cdot)\) | None | 0 | 2 |
| 2864.1.l | \(\chi_{2864}(357, \cdot)\) | 2864.1.l.a | 4 | 2 |
| 2864.1.n | \(\chi_{2864}(33, \cdot)\) | None | 0 | 88 |
| 2864.1.p | \(\chi_{2864}(39, \cdot)\) | None | 0 | 88 |
| 2864.1.r | \(\chi_{2864}(15, \cdot)\) | None | 0 | 88 |
| 2864.1.t | \(\chi_{2864}(41, \cdot)\) | None | 0 | 88 |
| 2864.1.u | \(\chi_{2864}(21, \cdot)\) | None | 0 | 176 |
| 2864.1.v | \(\chi_{2864}(3, \cdot)\) | None | 0 | 176 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2864))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2864)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(179))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(358))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(716))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1432))\)\(^{\oplus 2}\)