Defining parameters
| Level: | \( N \) | \(=\) | \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6300.in (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 700 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(2880\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6300, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 23296 | 9664 | 13632 |
| Cusp forms | 22784 | 9536 | 13248 |
| Eisenstein series | 512 | 128 | 384 |
Decomposition of \(S_{2}^{\mathrm{new}}(6300, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(6300, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)