Defining parameters
| Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8100.i (of order \(3\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
| Character field: | \(\Q(\zeta_{3})\) | ||
| Sturm bound: | \(3240\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8100, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3456 | 152 | 3304 |
| Cusp forms | 3024 | 152 | 2872 |
| Eisenstein series | 432 | 0 | 432 |
Decomposition of \(S_{2}^{\mathrm{new}}(8100, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8100, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)