Defining parameters
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.e (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(27, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 24 | 0 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 12 | 12 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(27, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
27.2.e.a | $12$ | $0.216$ | 12.0.\(\cdots\).1 | None | \(-6\) | \(-6\) | \(-3\) | \(-6\) | \(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\) |