Defining parameters
Level: | \( N \) | = | \( 32 = 2^{5} \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(32))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 272 | 149 | 123 |
Cusp forms | 240 | 139 | 101 |
Eisenstein series | 32 | 10 | 22 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)
We only show spaces with odd 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 \(S_{9}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)