Defining parameters
Level: | \( N \) | = | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 24 \) | ||
Sturm bound: | \(112896\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(735))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38592 | 25116 | 13476 |
Cusp forms | 36672 | 24536 | 12136 |
Eisenstein series | 1920 | 580 | 1340 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(735))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(735))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(735)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)