Defining parameters
Level: | \( N \) | = | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 16 \) | ||
Newform subspaces: | \( 32 \) | ||
Sturm bound: | \(6480\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(171))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2304 | 1779 | 525 |
Cusp forms | 2016 | 1625 | 391 |
Eisenstein series | 288 | 154 | 134 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(171))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(171))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(171)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)