Defining parameters
Level: | \( N \) | = | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | = | \( 5 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(3240\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(108))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1371 | 613 | 758 |
Cusp forms | 1221 | 581 | 640 |
Eisenstein series | 150 | 32 | 118 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(108))\)
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 available newforms together with their dimension.
Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces
\( S_{5}^{\mathrm{old}}(\Gamma_1(108)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)