Defining parameters
Level: | \( N \) | = | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(810\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(38))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 378 | 120 | 258 |
Cusp forms | 342 | 120 | 222 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(38))\)
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 |
---|---|---|---|---|
38.9.b | \(\chi_{38}(37, \cdot)\) | 38.9.b.a | 12 | 1 |
38.9.d | \(\chi_{38}(27, \cdot)\) | 38.9.d.a | 24 | 2 |
38.9.f | \(\chi_{38}(3, \cdot)\) | 38.9.f.a | 84 | 6 |
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)