Defining parameters
| Level: | \( N \) | = | \( 6041 = 7 \cdot 863 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(5958144\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6041))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1494708 | 1431773 | 62935 |
| Cusp forms | 1484365 | 1423161 | 61204 |
| Eisenstein series | 10343 | 8612 | 1731 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6041))\)
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 |
|---|---|---|---|---|
| 6041.2.a | \(\chi_{6041}(1, \cdot)\) | 6041.2.a.a | 1 | 1 |
| 6041.2.a.b | 2 | |||
| 6041.2.a.c | 83 | |||
| 6041.2.a.d | 101 | |||
| 6041.2.a.e | 112 | |||
| 6041.2.a.f | 132 | |||
| 6041.2.c | \(\chi_{6041}(6040, \cdot)\) | n/a | 574 | 1 |
| 6041.2.e | \(\chi_{6041}(3453, \cdot)\) | n/a | 1148 | 2 |
| 6041.2.g | \(\chi_{6041}(1725, \cdot)\) | n/a | 1148 | 2 |
| 6041.2.i | \(\chi_{6041}(8, \cdot)\) | n/a | 185760 | 430 |
| 6041.2.k | \(\chi_{6041}(13, \cdot)\) | n/a | 246820 | 430 |
| 6041.2.m | \(\chi_{6041}(2, \cdot)\) | n/a | 493640 | 860 |
| 6041.2.o | \(\chi_{6041}(5, \cdot)\) | n/a | 493640 | 860 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6041))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(863))\)\(^{\oplus 2}\)