Defining parameters
| Level: | \( N \) | = | \( 6044 = 2^{2} \cdot 1511 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(4566240\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6044))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1145335 | 667420 | 477915 |
| Cusp forms | 1137786 | 664400 | 473386 |
| Eisenstein series | 7549 | 3020 | 4529 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6044))\)
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 |
|---|---|---|---|---|
| 6044.2.a | \(\chi_{6044}(1, \cdot)\) | 6044.2.a.a | 63 | 1 |
| 6044.2.a.b | 63 | |||
| 6044.2.c | \(\chi_{6044}(6043, \cdot)\) | n/a | 754 | 1 |
| 6044.2.e | \(\chi_{6044}(2045, \cdot)\) | n/a | 504 | 4 |
| 6044.2.f | \(\chi_{6044}(423, \cdot)\) | n/a | 3016 | 4 |
| 6044.2.i | \(\chi_{6044}(9, \cdot)\) | n/a | 18900 | 150 |
| 6044.2.k | \(\chi_{6044}(55, \cdot)\) | n/a | 113100 | 150 |
| 6044.2.m | \(\chi_{6044}(5, \cdot)\) | n/a | 75600 | 600 |
| 6044.2.p | \(\chi_{6044}(11, \cdot)\) | n/a | 452400 | 600 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6044))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1511))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3022))\)\(^{\oplus 2}\)