Defining parameters
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Sturm bound: | \(672\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(576, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1184 | 122 | 1062 |
Cusp forms | 1120 | 118 | 1002 |
Eisenstein series | 64 | 4 | 60 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(576, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{7}^{\mathrm{old}}(576, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)