Defining parameters
Level: | \( N \) | = | \( 6728 = 2^{3} \cdot 29^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Sturm bound: | \(5651520\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6728))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1420104 | 795153 | 624951 |
Cusp forms | 1405657 | 790559 | 615098 |
Eisenstein series | 14447 | 4594 | 9853 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6728))\)
We only show spaces with even 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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6728))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6728)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1682))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3364))\)\(^{\oplus 2}\)