Defining parameters
| Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9200.do (of order \(22\) and degree \(10\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 115 \) |
| Character field: | \(\Q(\zeta_{22})\) | ||
| Sturm bound: | \(2880\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9200, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 14760 | 2180 | 12580 |
| Cusp forms | 14040 | 2140 | 11900 |
| Eisenstein series | 720 | 40 | 680 |
Decomposition of \(S_{2}^{\mathrm{new}}(9200, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(9200, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1840, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4600, [\chi])\)\(^{\oplus 2}\)