Defining parameters
Level: | \( N \) | = | \( 1734 = 2 \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(665856\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1734))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 251296 | 61993 | 189303 |
Cusp forms | 248096 | 61993 | 186103 |
Eisenstein series | 3200 | 0 | 3200 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1734))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1734))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1734)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 2}\)