Defining parameters
| Level: | \( N \) | \(=\) | \( 14400 = 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 14400.bx (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(5760\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(14400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5904 | 924 | 4980 |
| Cusp forms | 5616 | 900 | 4716 |
| Eisenstein series | 288 | 24 | 264 |
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
\( S_{2}^{\mathrm{old}}(14400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2880, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(7200, [\chi])\)\(^{\oplus 2}\)