Defining parameters
Level: | \( N \) | = | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 10 \) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(13440\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(232))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5208 | 2881 | 2327 |
Cusp forms | 4872 | 2773 | 2099 |
Eisenstein series | 336 | 108 | 228 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(232))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(232))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(232)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)