Defining parameters
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.eu (of order \(42\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 196 \) |
Character field: | \(\Q(\zeta_{42})\) | ||
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 | 20448 | 0 | 20448 |
Cusp forms | 19872 | 0 | 19872 |
Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{old}}(9800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4900, [\chi])\)\(^{\oplus 2}\)