Defining parameters
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(9\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(27, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9 | 3 | 6 |
Cusp forms | 3 | 3 | 0 |
Eisenstein series | 6 | 0 | 6 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
27.3.b.a | $1$ | $0.736$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(-13\) | \(q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots\) |
27.3.b.b | $2$ | $0.736$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(10\) | \(q+\beta q^{2}-5 q^{4}-\beta q^{5}+5 q^{7}-\beta q^{8}+\cdots\) |