Defining parameters
Level: | \( N \) | = | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 23 \) | ||
Sturm bound: | \(2880\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(99))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1160 | 880 | 280 |
Cusp forms | 1000 | 800 | 200 |
Eisenstein series | 160 | 80 | 80 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)
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.
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)