Defining parameters
| Level: | \( N \) | \(=\) | \( 4200 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4200.bk (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(1920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4200, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2016 | 216 | 1800 |
| Cusp forms | 1824 | 216 | 1608 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{new}}(4200, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4200, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)