Defining parameters
| Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9800.fg (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 175 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(3360\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 27392 | 4800 | 22592 |
| Cusp forms | 26368 | 4800 | 21568 |
| Eisenstein series | 1024 | 0 | 1024 |
Decomposition of \(S_{2}^{\mathrm{new}}(9800, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(9800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4900, [\chi])\)\(^{\oplus 2}\)