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: | \(\Q\) | ||
| Newforms: | \( 1 \) | ||
| 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 irreducible Hecke orbits
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 39.1.d.a | \(1\) | \(0.019\) | \(\Q\) | \(D_{2}\) | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) | \(\Q(\sqrt{13}) \) | \(0\) | \(-1\) | \(0\) | \(0\) | \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\) |