Defining parameters
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(21\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(27, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 14 | 28 |
Cusp forms | 30 | 10 | 20 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(27, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
27.7.d.a | $10$ | $6.211$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(3\) | \(0\) | \(219\) | \(-121\) | \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-5^{2}\beta _{4}+\beta _{5})q^{4}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(27, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)