Defining parameters
| Level: | \( N \) | \(=\) | \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 7200.cm (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(2880\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(7200, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5856 | 1532 | 4324 |
| Cusp forms | 5664 | 1508 | 4156 |
| Eisenstein series | 192 | 24 | 168 |
Decomposition of \(S_{2}^{\mathrm{new}}(7200, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(7200, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(7200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2400, [\chi])\)\(^{\oplus 2}\)