Defining parameters
| Level: | \( N \) | \(=\) | \( 12705 = 3 \cdot 5 \cdot 7 \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 12705.bt (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 33 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Sturm bound: | \(4224\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(12705, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8640 | 3456 | 5184 |
| Cusp forms | 8256 | 3456 | 4800 |
| Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{new}}(12705, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(12705, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(12705, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2541, [\chi])\)\(^{\oplus 2}\)