Defining parameters
Level: | \( N \) | = | \( 27 = 3^{3} \) |
Weight: | \( k \) | = | \( 36 \) |
Nonzero newspaces: | \( 3 \) | ||
Sturm bound: | \(1944\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_1(27))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 960 | 755 | 205 |
Cusp forms | 930 | 739 | 191 |
Eisenstein series | 30 | 16 | 14 |
Trace form
Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_1(27))\)
We only show spaces with even 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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces
\( S_{36}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 1}\)