Defining parameters
Level: | \( N \) | = | \( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 40 \) | ||
Sturm bound: | \(7160832\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8028))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1799088 | 828684 | 970404 |
Cusp forms | 1781329 | 824704 | 956625 |
Eisenstein series | 17759 | 3980 | 13779 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8028))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(8028))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(892))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4014))\)\(^{\oplus 2}\)