Defining parameters
Level: | \( N \) | = | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 18 \) | ||
Newform subspaces: | \( 65 \) | ||
Sturm bound: | \(36000\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(475))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9504 | 8598 | 906 |
Cusp forms | 8497 | 7902 | 595 |
Eisenstein series | 1007 | 696 | 311 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(475))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(475)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)