Defining parameters
| Level: | \( N \) | = | \( 3584 = 2^{9} \cdot 7 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Newform subspaces: | \( 14 \) | ||
| Sturm bound: | \(786432\) | ||
| Trace bound: | \(109\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3584))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5098 | 1256 | 3842 |
| Cusp forms | 490 | 136 | 354 |
| Eisenstein series | 4608 | 1120 | 3488 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 136 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3584))\)
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.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3584))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(3584)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(896))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1792))\)\(^{\oplus 2}\)