Defining parameters
| Level: | \( N \) | = | \( 6724 = 2^{2} \cdot 41^{2} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 16 \) | ||
| Sturm bound: | \(5648160\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6724))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1418140 | 825070 | 593070 |
| Cusp forms | 1405941 | 820350 | 585591 |
| Eisenstein series | 12199 | 4720 | 7479 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6724))\)
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 |
|---|---|---|---|---|
| 6724.2.a | \(\chi_{6724}(1, \cdot)\) | 6724.2.a.a | 3 | 1 |
| 6724.2.a.b | 3 | |||
| 6724.2.a.c | 4 | |||
| 6724.2.a.d | 4 | |||
| 6724.2.a.e | 6 | |||
| 6724.2.a.f | 8 | |||
| 6724.2.a.g | 8 | |||
| 6724.2.a.h | 12 | |||
| 6724.2.a.i | 12 | |||
| 6724.2.a.j | 16 | |||
| 6724.2.a.k | 18 | |||
| 6724.2.a.l | 18 | |||
| 6724.2.a.m | 24 | |||
| 6724.2.b | \(\chi_{6724}(3361, \cdot)\) | n/a | 136 | 1 |
| 6724.2.f | \(\chi_{6724}(4665, \cdot)\) | n/a | 274 | 2 |
| 6724.2.g | \(\chi_{6724}(857, \cdot)\) | n/a | 544 | 4 |
| 6724.2.i | \(\chi_{6724}(847, \cdot)\) | n/a | 3124 | 4 |
| 6724.2.k | \(\chi_{6724}(761, \cdot)\) | n/a | 544 | 4 |
| 6724.2.m | \(\chi_{6724}(3569, \cdot)\) | n/a | 1096 | 8 |
| 6724.2.o | \(\chi_{6724}(719, \cdot)\) | n/a | 12496 | 16 |
| 6724.2.q | \(\chi_{6724}(165, \cdot)\) | n/a | 5760 | 40 |
| 6724.2.t | \(\chi_{6724}(81, \cdot)\) | n/a | 5760 | 40 |
| 6724.2.u | \(\chi_{6724}(9, \cdot)\) | n/a | 11440 | 80 |
| 6724.2.w | \(\chi_{6724}(37, \cdot)\) | n/a | 23040 | 160 |
| 6724.2.x | \(\chi_{6724}(3, \cdot)\) | n/a | 137440 | 160 |
| 6724.2.ba | \(\chi_{6724}(25, \cdot)\) | n/a | 23040 | 160 |
| 6724.2.bd | \(\chi_{6724}(5, \cdot)\) | n/a | 45760 | 320 |
| 6724.2.bf | \(\chi_{6724}(7, \cdot)\) | n/a | 549760 | 640 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6724))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6724)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1681))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3362))\)\(^{\oplus 2}\)