Defining parameters
Level: | \( N \) | = | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 17 \) | ||
Sturm bound: | \(7260\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(242))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1975 | 596 | 1379 |
Cusp forms | 1656 | 596 | 1060 |
Eisenstein series | 319 | 0 | 319 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)