Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.p (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 96 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Sturm bound: | \(448\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1568 | 392 | 1176 |
Cusp forms | 1504 | 376 | 1128 |
Eisenstein series | 64 | 16 | 48 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{7}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)