Defining parameters
Level: | \( N \) | = | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 20 \) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(40320\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(435))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13888 | 9384 | 4504 |
Cusp forms | 12992 | 9056 | 3936 |
Eisenstein series | 896 | 328 | 568 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(435))\)
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.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(435))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(435)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 1}\)