Defining parameters
| Level: | \( N \) | = | \( 6561 = 3^{8} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(6377292\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6561))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1601613 | 1263276 | 338337 |
| Cusp forms | 1587034 | 1256148 | 330886 |
| Eisenstein series | 14579 | 7128 | 7451 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6561))\)
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 |
|---|---|---|---|---|
| 6561.2.a | \(\chi_{6561}(1, \cdot)\) | 6561.2.a.a | 36 | 1 |
| 6561.2.a.b | 36 | |||
| 6561.2.a.c | 72 | |||
| 6561.2.a.d | 72 | |||
| 6561.2.a.e | 90 | |||
| 6561.2.c | \(\chi_{6561}(2188, \cdot)\) | n/a | 612 | 2 |
| 6561.2.e | \(\chi_{6561}(730, \cdot)\) | n/a | 1836 | 6 |
| 6561.2.g | \(\chi_{6561}(244, \cdot)\) | n/a | 5670 | 18 |
| 6561.2.i | \(\chi_{6561}(82, \cdot)\) | n/a | 16848 | 54 |
| 6561.2.k | \(\chi_{6561}(28, \cdot)\) | n/a | 51840 | 162 |
| 6561.2.m | \(\chi_{6561}(10, \cdot)\) | n/a | 117612 | 486 |
| 6561.2.o | \(\chi_{6561}(4, \cdot)\) | n/a | 1061424 | 1458 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6561))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6561)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2187))\)\(^{\oplus 2}\)