Defining parameters
Level: | \( N \) | = | \( 132 = 2^{2} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(1920\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(132))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 580 | 222 | 358 |
Cusp forms | 381 | 190 | 191 |
Eisenstein series | 199 | 32 | 167 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)
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.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(132))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(132)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)