Defining parameters
| Level: | \( N \) | = | \( 6038 = 2 \cdot 3019 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Sturm bound: | \(4557180\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6038))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1142313 | 379764 | 762549 |
| Cusp forms | 1136278 | 379764 | 756514 |
| Eisenstein series | 6035 | 0 | 6035 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6038))\)
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 |
|---|---|---|---|---|
| 6038.2.a | \(\chi_{6038}(1, \cdot)\) | 6038.2.a.a | 2 | 1 |
| 6038.2.a.b | 54 | |||
| 6038.2.a.c | 57 | |||
| 6038.2.a.d | 69 | |||
| 6038.2.a.e | 70 | |||
| 6038.2.c | \(\chi_{6038}(239, \cdot)\) | n/a | 502 | 2 |
| 6038.2.e | \(\chi_{6038}(9, \cdot)\) | n/a | 127006 | 502 |
| 6038.2.g | \(\chi_{6038}(5, \cdot)\) | n/a | 252004 | 1004 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6038))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(3019))\)\(^{\oplus 2}\)