Defining parameters
Level: | \( N \) | = | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(35))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 98 | 22 |
Cusp forms | 72 | 70 | 2 |
Eisenstein series | 48 | 28 | 20 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 1}\)