Defining parameters
| Level: | \( N \) | \(=\) | \( 5616 = 2^{4} \cdot 3^{3} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5616.ba (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(2016\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5616, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2040 | 768 | 1272 |
| Cusp forms | 1992 | 768 | 1224 |
| Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{2}^{\mathrm{new}}(5616, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(5616, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5616, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1872, [\chi])\)\(^{\oplus 2}\)