Defining parameters
| Level: | \( N \) | = | \( 8006 = 2 \cdot 4003 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(8012004\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8006))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2007003 | 667666 | 1339337 |
| Cusp forms | 1999000 | 667666 | 1331334 |
| Eisenstein series | 8003 | 0 | 8003 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8006))\)
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 |
|---|---|---|---|---|
| 8006.2.a | \(\chi_{8006}(1, \cdot)\) | 8006.2.a.a | 69 | 1 |
| 8006.2.a.b | 75 | |||
| 8006.2.a.c | 92 | |||
| 8006.2.a.d | 98 | |||
| 8006.2.c | \(\chi_{8006}(4825, \cdot)\) | n/a | 666 | 2 |
| 8006.2.e | \(\chi_{8006}(551, \cdot)\) | n/a | 7370 | 22 |
| 8006.2.f | \(\chi_{8006}(203, \cdot)\) | n/a | 9380 | 28 |
| 8006.2.i | \(\chi_{8006}(129, \cdot)\) | n/a | 14652 | 44 |
| 8006.2.j | \(\chi_{8006}(117, \cdot)\) | n/a | 18648 | 56 |
| 8006.2.m | \(\chi_{8006}(11, \cdot)\) | n/a | 206360 | 616 |
| 8006.2.o | \(\chi_{8006}(7, \cdot)\) | n/a | 410256 | 1232 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8006))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(4003))\)\(^{\oplus 2}\)