Defining parameters
| Level: | \( N \) | = | \( 6078 = 2 \cdot 3 \cdot 1013 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 12 \) | ||
| Sturm bound: | \(4104672\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6078))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1030216 | 256543 | 773673 |
| Cusp forms | 1022121 | 256543 | 765578 |
| Eisenstein series | 8095 | 0 | 8095 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6078))\)
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 |
|---|---|---|---|---|
| 6078.2.a | \(\chi_{6078}(1, \cdot)\) | 6078.2.a.a | 1 | 1 |
| 6078.2.a.b | 1 | |||
| 6078.2.a.c | 2 | |||
| 6078.2.a.d | 14 | |||
| 6078.2.a.e | 15 | |||
| 6078.2.a.f | 17 | |||
| 6078.2.a.g | 19 | |||
| 6078.2.a.h | 22 | |||
| 6078.2.a.i | 23 | |||
| 6078.2.a.j | 27 | |||
| 6078.2.a.k | 28 | |||
| 6078.2.b | \(\chi_{6078}(4051, \cdot)\) | n/a | 170 | 1 |
| 6078.2.f | \(\chi_{6078}(4007, \cdot)\) | n/a | 676 | 2 |
| 6078.2.g | \(\chi_{6078}(739, \cdot)\) | n/a | 1680 | 10 |
| 6078.2.j | \(\chi_{6078}(475, \cdot)\) | n/a | 1700 | 10 |
| 6078.2.k | \(\chi_{6078}(121, \cdot)\) | n/a | 3696 | 22 |
| 6078.2.m | \(\chi_{6078}(65, \cdot)\) | n/a | 6760 | 20 |
| 6078.2.p | \(\chi_{6078}(427, \cdot)\) | n/a | 3740 | 22 |
| 6078.2.q | \(\chi_{6078}(95, \cdot)\) | n/a | 14872 | 44 |
| 6078.2.s | \(\chi_{6078}(19, \cdot)\) | n/a | 36960 | 220 |
| 6078.2.t | \(\chi_{6078}(13, \cdot)\) | n/a | 37400 | 220 |
| 6078.2.w | \(\chi_{6078}(5, \cdot)\) | n/a | 148720 | 440 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6078))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6078)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1013))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2026))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3039))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6078))\)\(^{\oplus 1}\)