Defining parameters
Level: | \( N \) | \(=\) | \( 4200 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4200.ew (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Sturm bound: | \(1920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4200, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4032 | 576 | 3456 |
Cusp forms | 3648 | 576 | 3072 |
Eisenstein series | 384 | 0 | 384 |
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
\( S_{2}^{\mathrm{old}}(4200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)