Defining parameters
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.j (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(9\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(39, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 2 | 12 |
Cusp forms | 6 | 2 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(39, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
39.2.j.a | $2$ | $0.311$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(0\) | \(-3\) | \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-2+4\zeta_{6})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(39, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(39, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)