Defining parameters
Level: | \( N \) | \(=\) | \( 4608 = 2^{9} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4608.bt (of order \(64\) and degree \(32\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 256 \) |
Character field: | \(\Q(\zeta_{64})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4608, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24832 | 0 | 24832 |
Cusp forms | 24320 | 0 | 24320 |
Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{old}}(4608, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)