Defining parameters
| Level: | \( N \) | \(=\) | \( 296 = 2^{3} \cdot 37 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 296.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 296 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(38\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(296, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 6 | 6 | 0 |
| Cusp forms | 4 | 4 | 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 | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(296, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 296.1.h.a | $2$ | $0.148$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-74}) \) | None | \(-2\) | \(-1\) | \(1\) | \(0\) | \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\) |
| 296.1.h.b | $2$ | $0.148$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-74}) \) | None | \(2\) | \(-1\) | \(-1\) | \(0\) | \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\) |