Defining parameters
Level: | \( N \) | = | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 10 \) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(150528\) | ||
Trace bound: | \(18\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1568))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2080 | 536 | 1544 |
Cusp forms | 160 | 51 | 109 |
Eisenstein series | 1920 | 485 | 1435 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 43 | 8 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1568))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(1568))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1568)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)