Defining parameters
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(504, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 304 | 0 | 304 |
Cusp forms | 272 | 0 | 272 |
Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{4}^{\mathrm{old}}(504, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)