Defining parameters
Level: | \( N \) | = | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(291600\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2025))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3138 | 1196 | 1942 |
Cusp forms | 114 | 48 | 66 |
Eisenstein series | 3024 | 1148 | 1876 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 32 | 0 | 0 | 16 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2025))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(2025))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2025)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)