Defining parameters
Level: | \( N \) | = | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 15 \) | ||
Newform subspaces: | \( 21 \) | ||
Sturm bound: | \(3024\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(117))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1104 | 840 | 264 |
Cusp forms | 912 | 740 | 172 |
Eisenstein series | 192 | 100 | 92 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(117))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(117)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 1}\)