Defining parameters
Level: | \( N \) | \(=\) | \( 9600 = 2^{7} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9600.fx (of order \(80\) and degree \(32\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1600 \) |
Character field: | \(\Q(\zeta_{80})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(3840\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 61696 | 0 | 61696 |
Cusp forms | 61184 | 0 | 61184 |
Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{old}}(9600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4800, [\chi])\)\(^{\oplus 2}\)