Defining parameters
| Level: | \( N \) | \(=\) | \( 14400 = 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 14400.gr (of order \(30\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 900 \) |
| Character field: | \(\Q(\zeta_{30})\) | ||
| Sturm bound: | \(5760\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(14400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 23232 | 5792 | 17440 |
| Cusp forms | 22848 | 5728 | 17120 |
| Eisenstein series | 384 | 64 | 320 |
Decomposition of \(S_{2}^{\mathrm{new}}(14400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(14400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(14400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(7200, [\chi])\)\(^{\oplus 2}\)