Defining parameters
Level: | \( N \) | = | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Sturm bound: | \(2004480\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4012))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 505760 | 291830 | 213930 |
Cusp forms | 496481 | 288414 | 208067 |
Eisenstein series | 9279 | 3416 | 5863 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4012))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(4012))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(4012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2006))\)\(^{\oplus 2}\)