Defining parameters
Level: | \( N \) | = | \( 19 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(19))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 114 | 112 | 2 |
Cusp forms | 96 | 96 | 0 |
Eisenstein series | 18 | 16 | 2 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)
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.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
19.8.a | \(\chi_{19}(1, \cdot)\) | 19.8.a.a | 4 | 1 |
19.8.a.b | 6 | |||
19.8.c | \(\chi_{19}(7, \cdot)\) | 19.8.c.a | 20 | 2 |
19.8.e | \(\chi_{19}(4, \cdot)\) | 19.8.e.a | 66 | 6 |