Defining parameters
Level: | \( N \) | = | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(8084220\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8042))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2025075 | 673684 | 1351391 |
Cusp forms | 2017036 | 673684 | 1343352 |
Eisenstein series | 8039 | 0 | 8039 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8042))\)
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 |
---|---|---|---|---|
8042.2.a | \(\chi_{8042}(1, \cdot)\) | 8042.2.a.a | 67 | 1 |
8042.2.a.b | 82 | |||
8042.2.a.c | 86 | |||
8042.2.a.d | 101 | |||
8042.2.b | \(\chi_{8042}(8041, \cdot)\) | n/a | 336 | 1 |
8042.2.c | \(\chi_{8042}(5833, \cdot)\) | n/a | 670 | 2 |
8042.2.e | \(\chi_{8042}(2401, \cdot)\) | n/a | 1348 | 4 |
8042.2.f | \(\chi_{8042}(1813, \cdot)\) | n/a | 668 | 2 |
8042.2.g | \(\chi_{8042}(49, \cdot)\) | n/a | 1344 | 4 |
8042.2.i | \(\chi_{8042}(37, \cdot)\) | n/a | 2680 | 8 |
8042.2.k | \(\chi_{8042}(329, \cdot)\) | n/a | 2672 | 8 |
8042.2.m | \(\chi_{8042}(67, \cdot)\) | n/a | 22242 | 66 |
8042.2.n | \(\chi_{8042}(13, \cdot)\) | n/a | 22176 | 66 |
8042.2.o | \(\chi_{8042}(77, \cdot)\) | n/a | 44220 | 132 |
8042.2.q | \(\chi_{8042}(27, \cdot)\) | n/a | 88968 | 264 |
8042.2.r | \(\chi_{8042}(53, \cdot)\) | n/a | 44088 | 132 |
8042.2.s | \(\chi_{8042}(17, \cdot)\) | n/a | 88704 | 264 |
8042.2.u | \(\chi_{8042}(3, \cdot)\) | n/a | 176880 | 528 |
8042.2.w | \(\chi_{8042}(39, \cdot)\) | n/a | 176352 | 528 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8042))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(4021))\)\(^{\oplus 2}\)