Defining parameters
Level: | \( N \) | = | \( 44 = 2^{2} \cdot 11 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(44))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 205 | 115 | 90 |
Cusp forms | 155 | 95 | 60 |
Eisenstein series | 50 | 20 | 30 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(44))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(44)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)