Defining parameters
Level: | \( N \) | = | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 24 \) | ||
Sturm bound: | \(591360\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2001))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 150304 | 111331 | 38973 |
Cusp forms | 145377 | 109067 | 36310 |
Eisenstein series | 4927 | 2264 | 2663 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2001))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(2001))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2001)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 2}\)