Defining parameters
Level: | \( N \) | = | \( 81 = 3^{4} \) |
Weight: | \( k \) | = | \( 12 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(5832\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(81))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2727 | 2140 | 587 |
Cusp forms | 2619 | 2084 | 535 |
Eisenstein series | 108 | 56 | 52 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(81))\)
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 |
---|---|---|---|---|
81.12.a | \(\chi_{81}(1, \cdot)\) | 81.12.a.a | 6 | 1 |
81.12.a.b | 6 | |||
81.12.a.c | 10 | |||
81.12.a.d | 10 | |||
81.12.a.e | 10 | |||
81.12.c | \(\chi_{81}(28, \cdot)\) | 81.12.c.a | 2 | 2 |
81.12.c.b | 2 | |||
81.12.c.c | 2 | |||
81.12.c.d | 2 | |||
81.12.c.e | 2 | |||
81.12.c.f | 4 | |||
81.12.c.g | 4 | |||
81.12.c.h | 8 | |||
81.12.c.i | 8 | |||
81.12.c.j | 8 | |||
81.12.c.k | 12 | |||
81.12.c.l | 12 | |||
81.12.c.m | 20 | |||
81.12.e | \(\chi_{81}(10, \cdot)\) | 81.12.e.a | 192 | 6 |
81.12.g | \(\chi_{81}(4, \cdot)\) | 81.12.g.a | 1764 | 18 |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)