Defining parameters
Level: | \( N \) | = | \( 558 = 2 \cdot 3^{2} \cdot 31 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Newform subspaces: | \( 63 \) | ||
Sturm bound: | \(34560\) | ||
Trace bound: | \(12\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(558))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9120 | 2276 | 6844 |
Cusp forms | 8161 | 2276 | 5885 |
Eisenstein series | 959 | 0 | 959 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(558))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(558))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(558)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 2}\)