Defining parameters
Level: | \( N \) | = | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(1944\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(108))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 723 | 315 | 408 |
Cusp forms | 573 | 283 | 290 |
Eisenstein series | 150 | 32 | 118 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)
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 the newforms together with their dimension.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(108)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)