Defining parameters
Level: | \( N \) | = | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 24 \) | ||
Sturm bound: | \(8064000\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8032))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2024000 | 1136454 | 887546 |
Cusp forms | 2008001 | 1131474 | 876527 |
Eisenstein series | 15999 | 4980 | 11019 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8032))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(8032))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8032)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2008))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4016))\)\(^{\oplus 2}\)