Defining parameters
Level: | \( N \) | = | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(36180\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(538))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9313 | 3014 | 6299 |
Cusp forms | 8778 | 3014 | 5764 |
Eisenstein series | 535 | 0 | 535 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(538))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(538))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(538)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(269))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(538))\)\(^{\oplus 1}\)