Defining parameters
| Level: | \( N \) | = | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 12 \) | ||
| Sturm bound: | \(1784832\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4008))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 450192 | 188890 | 261302 |
| Cusp forms | 442225 | 187570 | 254655 |
| Eisenstein series | 7967 | 1320 | 6647 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4008))\)
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 |
|---|---|---|---|---|
| 4008.2.a | \(\chi_{4008}(1, \cdot)\) | 4008.2.a.a | 1 | 1 |
| 4008.2.a.b | 1 | |||
| 4008.2.a.c | 1 | |||
| 4008.2.a.d | 1 | |||
| 4008.2.a.e | 3 | |||
| 4008.2.a.f | 5 | |||
| 4008.2.a.g | 7 | |||
| 4008.2.a.h | 8 | |||
| 4008.2.a.i | 9 | |||
| 4008.2.a.j | 10 | |||
| 4008.2.a.k | 11 | |||
| 4008.2.a.l | 12 | |||
| 4008.2.a.m | 13 | |||
| 4008.2.b | \(\chi_{4008}(2671, \cdot)\) | None | 0 | 1 |
| 4008.2.e | \(\chi_{4008}(335, \cdot)\) | None | 0 | 1 |
| 4008.2.f | \(\chi_{4008}(2005, \cdot)\) | n/a | 332 | 1 |
| 4008.2.i | \(\chi_{4008}(3005, \cdot)\) | n/a | 668 | 1 |
| 4008.2.j | \(\chi_{4008}(2339, \cdot)\) | n/a | 664 | 1 |
| 4008.2.m | \(\chi_{4008}(667, \cdot)\) | n/a | 336 | 1 |
| 4008.2.n | \(\chi_{4008}(1001, \cdot)\) | n/a | 168 | 1 |
| 4008.2.q | \(\chi_{4008}(25, \cdot)\) | n/a | 6888 | 82 |
| 4008.2.t | \(\chi_{4008}(17, \cdot)\) | n/a | 13776 | 82 |
| 4008.2.u | \(\chi_{4008}(43, \cdot)\) | n/a | 27552 | 82 |
| 4008.2.x | \(\chi_{4008}(11, \cdot)\) | n/a | 54776 | 82 |
| 4008.2.y | \(\chi_{4008}(5, \cdot)\) | n/a | 54776 | 82 |
| 4008.2.bb | \(\chi_{4008}(61, \cdot)\) | n/a | 27552 | 82 |
| 4008.2.bc | \(\chi_{4008}(47, \cdot)\) | None | 0 | 82 |
| 4008.2.bf | \(\chi_{4008}(55, \cdot)\) | None | 0 | 82 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4008))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(4008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)\(^{\oplus 2}\)