Defining parameters
Level: | \( N \) | = | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 10 \) | ||
Newform subspaces: | \( 44 \) | ||
Sturm bound: | \(9600\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(200))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3768 | 1908 | 1860 |
Cusp forms | 3432 | 1826 | 1606 |
Eisenstein series | 336 | 82 | 254 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(200))\)
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.
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(200)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)