Defining parameters
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(4\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(39, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3 | 3 | 0 |
Cusp forms | 1 | 1 | 0 |
Eisenstein series | 2 | 2 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 1 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(39, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
39.1.d.a | $1$ | $0.019$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) | \(\Q(\sqrt{13}) \) | \(0\) | \(-1\) | \(0\) | \(0\) | \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\) |