Defining parameters
Level: | \( N \) | = | \( 1161 = 3^{3} \cdot 43 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(99792\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1161))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1332 | 696 | 636 |
Cusp forms | 72 | 40 | 32 |
Eisenstein series | 1260 | 656 | 604 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 28 | 0 | 4 | 8 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1161))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(1161))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1161)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(387))\)\(^{\oplus 2}\)