Defining parameters
Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8400.gc (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 560 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Sturm bound: | \(3840\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7776 | 2304 | 5472 |
Cusp forms | 7584 | 2304 | 5280 |
Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{new}}(8400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2800, [\chi])\)\(^{\oplus 2}\)