Defining parameters
Level: | \( N \) | = | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 9 \) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(7776\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(216))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2772 | 1184 | 1588 |
Cusp forms | 2412 | 1120 | 1292 |
Eisenstein series | 360 | 64 | 296 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(216))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(216))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(216)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)