Defining parameters
Level: | \( N \) | = | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 18 \) | ||
Sturm bound: | \(54000\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(475))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18504 | 16847 | 1657 |
Cusp forms | 17496 | 16149 | 1347 |
Eisenstein series | 1008 | 698 | 310 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(475))\)
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 available newforms together with their dimension.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(475))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(475)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)