Defining parameters
| Level: | \( N \) | = | \( 8038 = 2 \cdot 4019 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Sturm bound: | \(8076180\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8038))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2023063 | 673014 | 1350049 |
| Cusp forms | 2015028 | 673014 | 1342014 |
| Eisenstein series | 8035 | 0 | 8035 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8038))\)
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 |
|---|---|---|---|---|
| 8038.2.a | \(\chi_{8038}(1, \cdot)\) | 8038.2.a.a | 75 | 1 |
| 8038.2.a.b | 83 | |||
| 8038.2.a.c | 84 | |||
| 8038.2.a.d | 92 | |||
| 8038.2.c | \(\chi_{8038}(273, \cdot)\) | n/a | 2010 | 6 |
| 8038.2.e | \(\chi_{8038}(135, \cdot)\) | n/a | 13400 | 40 |
| 8038.2.f | \(\chi_{8038}(3, \cdot)\) | n/a | 14070 | 42 |
| 8038.2.i | \(\chi_{8038}(41, \cdot)\) | n/a | 80400 | 240 |
| 8038.2.k | \(\chi_{8038}(5, \cdot)\) | n/a | 562800 | 1680 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8038))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(4019))\)\(^{\oplus 2}\)