Defining parameters
| Level: | \( N \) | \(=\) | \( 14400 = 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 14400.im (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 900 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(5760\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(14400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 46464 | 11584 | 34880 |
| Cusp forms | 45696 | 11456 | 34240 |
| Eisenstein series | 768 | 128 | 640 |
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
\( S_{2}^{\mathrm{old}}(14400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(7200, [\chi])\)\(^{\oplus 2}\)