Defining parameters
Level: | \( N \) | = | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Sturm bound: | \(8004000\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8002))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2005000 | 666999 | 1338001 |
Cusp forms | 1997001 | 666999 | 1330002 |
Eisenstein series | 7999 | 0 | 7999 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8002))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(8002))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(4001))\)\(^{\oplus 2}\)