Defining parameters
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.f (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(198, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 464 | 60 | 404 |
Cusp forms | 400 | 60 | 340 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(198, [\chi])\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(198, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(198, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)