Defining parameters
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.bh (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3200, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 136 | 0 | 136 |
Cusp forms | 72 | 0 | 72 |
Eisenstein series | 64 | 0 | 64 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 0 | 0 | 0 |
Decomposition of \(S_{1}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)