Defining parameters
Level: | \( N \) | = | \( 3002 = 2 \cdot 19 \cdot 79 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 32 \) | ||
Sturm bound: | \(1123200\) | ||
Trace bound: | \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3002))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 283608 | 93053 | 190555 |
Cusp forms | 277993 | 93053 | 184940 |
Eisenstein series | 5615 | 0 | 5615 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3002))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(3002))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(3002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1501))\)\(^{\oplus 2}\)