Defining parameters
Level: | \( N \) | = | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(36))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 21 | 35 |
Cusp forms | 17 | 13 | 4 |
Eisenstein series | 39 | 8 | 31 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)