Defining parameters
Level: | \( N \) | = | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 41 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1312\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{41}(\Gamma_1(21))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 652 | 458 | 194 |
Cusp forms | 628 | 450 | 178 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{41}^{\mathrm{new}}(\Gamma_1(21))\)
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 the newforms together with their dimension.
Decomposition of \(S_{41}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces
\( S_{41}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{41}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{41}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)