Defining parameters
| Level: | \( N \) | \(=\) | \( 21168 = 2^{4} \cdot 3^{3} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 21168.gp (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 108 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Sturm bound: | \(8064\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(21168, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 24480 | 4428 | 20052 |
| Cusp forms | 23904 | 4428 | 19476 |
| Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{new}}(21168, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(21168, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(21168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3024, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(5292, [\chi])\)\(^{\oplus 3}\)