Defining parameters
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.cg (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 76 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Sturm bound: | \(360\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1488 | 612 | 876 |
Cusp forms | 1392 | 588 | 804 |
Eisenstein series | 96 | 24 | 72 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)