Defining parameters
| Level: | \( N \) | = | \( 4006 = 2 \cdot 2003 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(2006004\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4006))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 503503 | 167166 | 336337 |
| Cusp forms | 499500 | 167166 | 332334 |
| Eisenstein series | 4003 | 0 | 4003 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4006))\)
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 |
|---|---|---|---|---|
| 4006.2.a | \(\chi_{4006}(1, \cdot)\) | 4006.2.a.a | 1 | 1 |
| 4006.2.a.b | 1 | |||
| 4006.2.a.c | 1 | |||
| 4006.2.a.d | 2 | |||
| 4006.2.a.e | 2 | |||
| 4006.2.a.f | 31 | |||
| 4006.2.a.g | 40 | |||
| 4006.2.a.h | 42 | |||
| 4006.2.a.i | 46 | |||
| 4006.2.c | \(\chi_{4006}(485, \cdot)\) | n/a | 1002 | 6 |
| 4006.2.d | \(\chi_{4006}(523, \cdot)\) | n/a | 1670 | 10 |
| 4006.2.e | \(\chi_{4006}(89, \cdot)\) | n/a | 2004 | 12 |
| 4006.2.i | \(\chi_{4006}(57, \cdot)\) | n/a | 10020 | 60 |
| 4006.2.j | \(\chi_{4006}(53, \cdot)\) | n/a | 12024 | 72 |
| 4006.2.k | \(\chi_{4006}(113, \cdot)\) | n/a | 20040 | 120 |
| 4006.2.o | \(\chi_{4006}(3, \cdot)\) | n/a | 120240 | 720 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4006))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(4006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2003))\)\(^{\oplus 2}\)