Defining parameters
Level: | \( N \) | = | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 16 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(512\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(21))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 252 | 182 | 70 |
Cusp forms | 228 | 170 | 58 |
Eisenstein series | 24 | 12 | 12 |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(21))\)
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 \(S_{16}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)