Defining parameters
Level: | \( N \) | = | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(2022060\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4022))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 507525 | 168504 | 339021 |
Cusp forms | 503506 | 168504 | 335002 |
Eisenstein series | 4019 | 0 | 4019 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4022))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
4022.2.a | \(\chi_{4022}(1, \cdot)\) | 4022.2.a.a | 1 | 1 |
4022.2.a.b | 3 | |||
4022.2.a.c | 31 | |||
4022.2.a.d | 37 | |||
4022.2.a.e | 46 | |||
4022.2.a.f | 50 | |||
4022.2.c | \(\chi_{4022}(205, \cdot)\) | n/a | 334 | 2 |
4022.2.d | \(\chi_{4022}(2809, \cdot)\) | n/a | 676 | 4 |
4022.2.g | \(\chi_{4022}(699, \cdot)\) | n/a | 1336 | 8 |
4022.2.i | \(\chi_{4022}(103, \cdot)\) | n/a | 11154 | 66 |
4022.2.k | \(\chi_{4022}(115, \cdot)\) | n/a | 22044 | 132 |
4022.2.l | \(\chi_{4022}(13, \cdot)\) | n/a | 44616 | 264 |
4022.2.o | \(\chi_{4022}(5, \cdot)\) | n/a | 88176 | 528 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4022))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(4022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2011))\)\(^{\oplus 2}\)