Defining parameters
| Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8100.co (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 225 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(3240\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8100, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 26496 | 1920 | 24576 |
| Cusp forms | 25344 | 1920 | 23424 |
| Eisenstein series | 1152 | 0 | 1152 |
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
\( S_{2}^{\mathrm{old}}(8100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)