Defining parameters
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.ca (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1760 | 432 | 1328 |
Cusp forms | 1696 | 432 | 1264 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)