Defining parameters
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.g (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(189, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 52 | 104 |
Cusp forms | 132 | 44 | 88 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(189, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
189.4.g.a | $44$ | $11.151$ | None | \(-1\) | \(0\) | \(-38\) | \(-7\) |
Decomposition of \(S_{4}^{\mathrm{old}}(189, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)