Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.s (of order \(16\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 192 \) |
Character field: | \(\Q(\zeta_{16})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(640\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4640 | 0 | 4640 |
Cusp forms | 4576 | 0 | 4576 |
Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{10}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)