Defining parameters
Level: | \( N \) | = | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 21 \) | ||
Sturm bound: | \(5760\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(165))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2080 | 1356 | 724 |
Cusp forms | 1760 | 1244 | 516 |
Eisenstein series | 320 | 112 | 208 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(165))\)
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 the newforms together with their dimension.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(165)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)