Defining parameters
| Level: | \( N \) | \(=\) | \( 3648 = 2^{6} \cdot 3 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3648.dl (of order \(36\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 304 \) |
| Character field: | \(\Q(\zeta_{36})\) | ||
| Sturm bound: | \(1280\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3648, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 7872 | 960 | 6912 |
| Cusp forms | 7488 | 960 | 6528 |
| Eisenstein series | 384 | 0 | 384 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3648, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1824, [\chi])\)\(^{\oplus 2}\)