Defining parameters
Level: | \( N \) | = | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(35))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 228 | 36 |
Cusp forms | 216 | 196 | 20 |
Eisenstein series | 48 | 32 | 16 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)
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.
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 1}\)