Defining parameters
| Level: | \( N \) | \(=\) | \( 1412 = 2^{2} \cdot 353 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1412.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1412 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(177\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1412, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9 | 9 | 0 |
| Cusp forms | 7 | 7 | 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 | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1412, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1412.1.d.a | $1$ | $0.705$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-353}) \) | \(\Q(\sqrt{353}) \) | \(1\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}+2q^{17}+\cdots\) |
| 1412.1.d.b | $2$ | $0.705$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-353}) \) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{8}+\cdots\) |
| 1412.1.d.c | $4$ | $0.705$ | \(\Q(\zeta_{16})^+\) | $D_{8}$ | \(\Q(\sqrt{-353}) \) | None | \(-4\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{3}q^{7}+\cdots\) |