Defining parameters
| Level: | \( N \) | = | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 16 \) | ||
| Sturm bound: | \(4015872\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6012))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1010608 | 465090 | 545518 |
| Cusp forms | 997329 | 462118 | 535211 |
| Eisenstein series | 13279 | 2972 | 10307 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6012))\)
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 |
|---|---|---|---|---|
| 6012.2.a | \(\chi_{6012}(1, \cdot)\) | 6012.2.a.a | 2 | 1 |
| 6012.2.a.b | 3 | |||
| 6012.2.a.c | 3 | |||
| 6012.2.a.d | 5 | |||
| 6012.2.a.e | 5 | |||
| 6012.2.a.f | 5 | |||
| 6012.2.a.g | 7 | |||
| 6012.2.a.h | 9 | |||
| 6012.2.a.i | 9 | |||
| 6012.2.a.j | 10 | |||
| 6012.2.a.k | 10 | |||
| 6012.2.b | \(\chi_{6012}(667, \cdot)\) | n/a | 418 | 1 |
| 6012.2.c | \(\chi_{6012}(2339, \cdot)\) | n/a | 332 | 1 |
| 6012.2.h | \(\chi_{6012}(3005, \cdot)\) | 6012.2.h.a | 56 | 1 |
| 6012.2.i | \(\chi_{6012}(2005, \cdot)\) | n/a | 332 | 2 |
| 6012.2.j | \(\chi_{6012}(1001, \cdot)\) | n/a | 336 | 2 |
| 6012.2.o | \(\chi_{6012}(335, \cdot)\) | n/a | 1992 | 2 |
| 6012.2.p | \(\chi_{6012}(2671, \cdot)\) | n/a | 2008 | 2 |
| 6012.2.q | \(\chi_{6012}(181, \cdot)\) | n/a | 5740 | 82 |
| 6012.2.r | \(\chi_{6012}(17, \cdot)\) | n/a | 4592 | 82 |
| 6012.2.w | \(\chi_{6012}(107, \cdot)\) | n/a | 27552 | 82 |
| 6012.2.x | \(\chi_{6012}(55, \cdot)\) | n/a | 34276 | 82 |
| 6012.2.y | \(\chi_{6012}(25, \cdot)\) | n/a | 27552 | 164 |
| 6012.2.z | \(\chi_{6012}(43, \cdot)\) | n/a | 164656 | 164 |
| 6012.2.ba | \(\chi_{6012}(11, \cdot)\) | n/a | 164656 | 164 |
| 6012.2.bf | \(\chi_{6012}(5, \cdot)\) | n/a | 27552 | 164 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6012))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3006))\)\(^{\oplus 2}\)