Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.u (of order \(32\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 128 \) |
Character field: | \(\Q(\zeta_{32})\) | ||
Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8224 | 4096 | 4128 |
Cusp forms | 8160 | 4096 | 4064 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{9}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)