Defining parameters
| Level: | \( N \) | = | \( 6627 = 3 \cdot 47^{2} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(6503296\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6627))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1632264 | 1221393 | 410871 |
| Cusp forms | 1619385 | 1215137 | 404248 |
| Eisenstein series | 12879 | 6256 | 6623 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6627))\)
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 |
|---|---|---|---|---|
| 6627.2.a | \(\chi_{6627}(1, \cdot)\) | 6627.2.a.a | 1 | 1 |
| 6627.2.a.b | 1 | |||
| 6627.2.a.c | 1 | |||
| 6627.2.a.d | 1 | |||
| 6627.2.a.e | 1 | |||
| 6627.2.a.f | 1 | |||
| 6627.2.a.g | 1 | |||
| 6627.2.a.h | 1 | |||
| 6627.2.a.i | 1 | |||
| 6627.2.a.j | 2 | |||
| 6627.2.a.k | 2 | |||
| 6627.2.a.l | 2 | |||
| 6627.2.a.m | 2 | |||
| 6627.2.a.n | 2 | |||
| 6627.2.a.o | 3 | |||
| 6627.2.a.p | 3 | |||
| 6627.2.a.q | 3 | |||
| 6627.2.a.r | 3 | |||
| 6627.2.a.s | 4 | |||
| 6627.2.a.t | 4 | |||
| 6627.2.a.u | 4 | |||
| 6627.2.a.v | 4 | |||
| 6627.2.a.w | 4 | |||
| 6627.2.a.x | 4 | |||
| 6627.2.a.y | 6 | |||
| 6627.2.a.z | 8 | |||
| 6627.2.a.ba | 12 | |||
| 6627.2.a.bb | 16 | |||
| 6627.2.a.bc | 16 | |||
| 6627.2.a.bd | 32 | |||
| 6627.2.a.be | 40 | |||
| 6627.2.a.bf | 44 | |||
| 6627.2.a.bg | 44 | |||
| 6627.2.a.bh | 44 | |||
| 6627.2.a.bi | 44 | |||
| 6627.2.c | \(\chi_{6627}(6626, \cdot)\) | n/a | 676 | 1 |
| 6627.2.e | \(\chi_{6627}(202, \cdot)\) | n/a | 7920 | 22 |
| 6627.2.g | \(\chi_{6627}(116, \cdot)\) | n/a | 14872 | 22 |
| 6627.2.i | \(\chi_{6627}(142, \cdot)\) | n/a | 17296 | 46 |
| 6627.2.k | \(\chi_{6627}(140, \cdot)\) | n/a | 34500 | 46 |
| 6627.2.m | \(\chi_{6627}(4, \cdot)\) | n/a | 380512 | 1012 |
| 6627.2.o | \(\chi_{6627}(5, \cdot)\) | n/a | 759000 | 1012 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6627))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6627)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2209))\)\(^{\oplus 2}\)