Defining parameters
| Level: | \( N \) | = | \( 4021 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 16 \) | ||
| Sturm bound: | \(2694740\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4021))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 675695 | 675695 | 0 |
| Cusp forms | 671676 | 671676 | 0 |
| Eisenstein series | 4019 | 4019 | 0 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4021))\)
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 |
|---|---|---|---|---|
| 4021.2.a | \(\chi_{4021}(1, \cdot)\) | 4021.2.a.a | 1 | 1 |
| 4021.2.a.b | 151 | |||
| 4021.2.a.c | 182 | |||
| 4021.2.b | \(\chi_{4021}(4020, \cdot)\) | n/a | 334 | 1 |
| 4021.2.c | \(\chi_{4021}(1812, \cdot)\) | n/a | 668 | 2 |
| 4021.2.e | \(\chi_{4021}(2401, \cdot)\) | n/a | 1332 | 4 |
| 4021.2.f | \(\chi_{4021}(1813, \cdot)\) | n/a | 670 | 2 |
| 4021.2.g | \(\chi_{4021}(49, \cdot)\) | n/a | 1336 | 4 |
| 4021.2.i | \(\chi_{4021}(37, \cdot)\) | n/a | 2672 | 8 |
| 4021.2.k | \(\chi_{4021}(110, \cdot)\) | n/a | 2680 | 8 |
| 4021.2.m | \(\chi_{4021}(67, \cdot)\) | n/a | 21978 | 66 |
| 4021.2.n | \(\chi_{4021}(13, \cdot)\) | n/a | 22044 | 66 |
| 4021.2.o | \(\chi_{4021}(77, \cdot)\) | n/a | 44088 | 132 |
| 4021.2.q | \(\chi_{4021}(27, \cdot)\) | n/a | 87912 | 264 |
| 4021.2.r | \(\chi_{4021}(53, \cdot)\) | n/a | 44220 | 132 |
| 4021.2.s | \(\chi_{4021}(17, \cdot)\) | n/a | 88176 | 264 |
| 4021.2.u | \(\chi_{4021}(3, \cdot)\) | n/a | 176352 | 528 |
| 4021.2.w | \(\chi_{4021}(4, \cdot)\) | n/a | 176880 | 528 |
"n/a" means that newforms for that character have not been added to the database yet