Defining parameters
Level: | \( N \) | = | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 28 \) | ||
Sturm bound: | \(860160\) | ||
Trace bound: | \(15\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1856))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 324576 | 181602 | 142974 |
Cusp forms | 320544 | 180414 | 140130 |
Eisenstein series | 4032 | 1188 | 2844 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1856))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(1856))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1856)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(928))\)\(^{\oplus 2}\)