Defining parameters
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.bm (of order \(16\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 64 \) |
Character field: | \(\Q(\zeta_{16})\) | ||
Sturm bound: | \(480\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1968 | 1240 | 728 |
Cusp forms | 1872 | 1192 | 680 |
Eisenstein series | 96 | 48 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)