Defining parameters
| Level: | \( N \) | = | \( 6007 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 16 \) | ||
| Sturm bound: | \(6014008\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6007))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1506505 | 1506505 | 0 |
| Cusp forms | 1500500 | 1500500 | 0 |
| Eisenstein series | 6005 | 6005 | 0 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6007))\)
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 |
|---|---|---|---|---|
| 6007.2.a | \(\chi_{6007}(1, \cdot)\) | 6007.2.a.a | 2 | 1 |
| 6007.2.a.b | 237 | |||
| 6007.2.a.c | 261 | |||
| 6007.2.c | \(\chi_{6007}(77, \cdot)\) | n/a | 1000 | 2 |
| 6007.2.e | \(\chi_{6007}(295, \cdot)\) | n/a | 2994 | 6 |
| 6007.2.f | \(\chi_{6007}(391, \cdot)\) | n/a | 4990 | 10 |
| 6007.2.g | \(\chi_{6007}(454, \cdot)\) | n/a | 5988 | 12 |
| 6007.2.i | \(\chi_{6007}(183, \cdot)\) | n/a | 6000 | 12 |
| 6007.2.l | \(\chi_{6007}(72, \cdot)\) | n/a | 10000 | 20 |
| 6007.2.m | \(\chi_{6007}(232, \cdot)\) | n/a | 12000 | 24 |
| 6007.2.p | \(\chi_{6007}(421, \cdot)\) | n/a | 29940 | 60 |
| 6007.2.r | \(\chi_{6007}(138, \cdot)\) | n/a | 35928 | 72 |
| 6007.2.s | \(\chi_{6007}(38, \cdot)\) | n/a | 59880 | 120 |
| 6007.2.v | \(\chi_{6007}(49, \cdot)\) | n/a | 60000 | 120 |
| 6007.2.w | \(\chi_{6007}(140, \cdot)\) | n/a | 72000 | 144 |
| 6007.2.y | \(\chi_{6007}(41, \cdot)\) | n/a | 120000 | 240 |
| 6007.2.bc | \(\chi_{6007}(2, \cdot)\) | n/a | 359280 | 720 |
| 6007.2.be | \(\chi_{6007}(9, \cdot)\) | n/a | 720000 | 1440 |
"n/a" means that newforms for that character have not been added to the database yet