Defining parameters
| Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 392.g (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(56\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(392, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 11 | 8 | 3 |
| Cusp forms | 3 | 3 | 0 |
| Eisenstein series | 8 | 5 | 3 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(392, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 392.1.g.a | \(1\) | \(0.196\) | \(\Q\) | \(D_{2}\) | \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{14}) \) | \(1\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots\) |
| 392.1.g.b | \(2\) | \(0.196\) | \(\Q(\sqrt{2}) \) | \(D_{4}\) | \(\Q(\sqrt{-2}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots\) |