Defining parameters
| Level: | \( N \) | \(=\) | \( 9300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 31 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9300.kz (of order \(30\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 775 \) |
| Character field: | \(\Q(\zeta_{30})\) | ||
| Sturm bound: | \(3840\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9300, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 15456 | 1280 | 14176 |
| Cusp forms | 15264 | 1280 | 13984 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{new}}(9300, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(9300, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9300, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4650, [\chi])\)\(^{\oplus 2}\)