Defining parameters
Level: | \( N \) | = | \( 27 = 3^{3} \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(378\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(27))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 177 | 136 | 41 |
Cusp forms | 147 | 120 | 27 |
Eisenstein series | 30 | 16 | 14 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)
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 \(S_{7}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 1}\)