Defining parameters
| Level: | \( N \) | = | \( 81 = 3^{4} \) |
| Weight: | \( k \) | = | \( 10 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 19 \) | ||
| Sturm bound: | \(4860\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(81))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2241 | 1756 | 485 |
| Cusp forms | 2133 | 1700 | 433 |
| Eisenstein series | 108 | 56 | 52 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(81))\)
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 |
|---|---|---|---|---|
| 81.10.a | \(\chi_{81}(1, \cdot)\) | 81.10.a.a | 4 | 1 |
| 81.10.a.b | 4 | |||
| 81.10.a.c | 8 | |||
| 81.10.a.d | 8 | |||
| 81.10.a.e | 10 | |||
| 81.10.c | \(\chi_{81}(28, \cdot)\) | 81.10.c.a | 2 | 2 |
| 81.10.c.b | 2 | |||
| 81.10.c.c | 2 | |||
| 81.10.c.d | 2 | |||
| 81.10.c.e | 2 | |||
| 81.10.c.f | 4 | |||
| 81.10.c.g | 6 | |||
| 81.10.c.h | 6 | |||
| 81.10.c.i | 8 | |||
| 81.10.c.j | 8 | |||
| 81.10.c.k | 8 | |||
| 81.10.c.l | 20 | |||
| 81.10.e | \(\chi_{81}(10, \cdot)\) | 81.10.e.a | 156 | 6 |
| 81.10.g | \(\chi_{81}(4, \cdot)\) | 81.10.g.a | 1440 | 18 |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)