Defining parameters
Level: | \( N \) | = | \( 261 = 3^{2} \cdot 29 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 17 \) | ||
Sturm bound: | \(15120\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(261))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5264 | 4104 | 1160 |
Cusp forms | 4816 | 3860 | 956 |
Eisenstein series | 448 | 244 | 204 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(261))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(261)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)