Defining parameters
Level: | \( N \) | = | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(883200\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3525))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5496 | 2036 | 3460 |
Cusp forms | 344 | 192 | 152 |
Eisenstein series | 5152 | 1844 | 3308 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 192 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3525))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3525))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(3525)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(705))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1175))\)\(^{\oplus 2}\)