Defining parameters
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.bd (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(3360\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3552 | 0 | 3552 |
Cusp forms | 3168 | 0 | 3168 |
Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{old}}(9800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)