Defining parameters
Level: | \( N \) | = | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 40 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(1280\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{40}(\Gamma_1(21))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 636 | 462 | 174 |
Cusp forms | 612 | 450 | 162 |
Eisenstein series | 24 | 12 | 12 |
Trace form
Decomposition of \(S_{40}^{\mathrm{new}}(\Gamma_1(21))\)
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 the newforms together with their dimension.
Decomposition of \(S_{40}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces
\( S_{40}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{40}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{40}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{40}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)