Defining parameters
Level: | \( N \) | = | \( 81 = 3^{4} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(1458\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(81))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 540 | 412 | 128 |
Cusp forms | 432 | 356 | 76 |
Eisenstein series | 108 | 56 | 52 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(81))\)
We only show spaces with odd 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.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)