Defining parameters
| Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2400.dl (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Sturm bound: | \(960\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3968 | 480 | 3488 |
| Cusp forms | 3712 | 480 | 3232 |
| Eisenstein series | 256 | 0 | 256 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)