Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.v (of order \(32\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 128 \) |
Character field: | \(\Q(\zeta_{32})\) | ||
Sturm bound: | \(640\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9248 | 4608 | 4640 |
Cusp forms | 9184 | 4608 | 4576 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{10}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)