Defining parameters
Level: | \( N \) | = | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 5 \) |
Nonzero newspaces: | \( 18 \) | ||
Sturm bound: | \(162000\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(675))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 65640 | 47517 | 18123 |
Cusp forms | 63960 | 46861 | 17099 |
Eisenstein series | 1680 | 656 | 1024 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(675))\)
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 \(S_{5}^{\mathrm{old}}(\Gamma_1(675))\) into lower level spaces
\( S_{5}^{\mathrm{old}}(\Gamma_1(675)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)