Defining parameters
Level: | \( N \) | = | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(36))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 53 | 75 |
Cusp forms | 88 | 45 | 43 |
Eisenstein series | 40 | 8 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)
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 the newforms together with their dimension.
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)