Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 342 | 54 | 288 |
Cusp forms | 306 | 54 | 252 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
108.4.i.a | $54$ | $6.372$ | None | \(0\) | \(0\) | \(12\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)