Defining parameters
| Level: | \( N \) | \(=\) | \( 155 = 5 \cdot 31 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 155.c (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 155 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(16\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(155, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5 | 5 | 0 |
| Cusp forms | 3 | 3 | 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 | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(155, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 155.1.c.a | \(1\) | \(0.077\) | \(\Q\) | \(D_{2}\) | \(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(-1\) | \(0\) | \(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\) |
| 155.1.c.b | \(2\) | \(0.077\) | \(\Q(\sqrt{-3}) \) | \(D_{6}\) | \(\Q(\sqrt{-31}) \) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\) |