Defining parameters
Level: | \( N \) | = | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(270\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(22))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 130 | 40 | 90 |
Cusp forms | 110 | 40 | 70 |
Eisenstein series | 20 | 0 | 20 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(22))\)
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.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
22.9.b | \(\chi_{22}(21, \cdot)\) | 22.9.b.a | 8 | 1 |
22.9.d | \(\chi_{22}(7, \cdot)\) | 22.9.d.a | 32 | 4 |
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)