Defining parameters
Level: | \( N \) | = | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(1039680\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2166))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 391896 | 96931 | 294965 |
Cusp forms | 387864 | 96931 | 290933 |
Eisenstein series | 4032 | 0 | 4032 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2166))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2166))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(2166)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)