Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.o (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 96 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Sturm bound: | \(256\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 800 | 200 | 600 |
Cusp forms | 736 | 184 | 552 |
Eisenstein series | 64 | 16 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)