Defining parameters
| Level: | \( N \) | = | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Character orbit: | \([\chi]\) | = | 276.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 276 \) |
| Character field: | \(\Q\) | ||
| Newforms: | \( 4 \) | ||
| Sturm bound: | \(48\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(276, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 10 | 10 | 0 |
| Cusp forms | 6 | 6 | 0 |
| Eisenstein series | 4 | 4 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(276, [\chi])\) into irreducible Hecke orbits
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 276.1.h.a | \(1\) | \(0.138\) | \(\Q\) | \(D_{2}\) | \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \) | \(\Q(\sqrt{3}) \) | \(-1\) | \(1\) | \(0\) | \(0\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\) |
| 276.1.h.b | \(1\) | \(0.138\) | \(\Q\) | \(D_{2}\) | \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \) | \(\Q(\sqrt{3}) \) | \(1\) | \(-1\) | \(0\) | \(0\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\) |
| 276.1.h.c | \(2\) | \(0.138\) | \(\Q(\sqrt{-3}) \) | \(D_{6}\) | \(\Q(\sqrt{-23}) \) | None | \(-1\) | \(1\) | \(0\) | \(0\) | \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\) |
| 276.1.h.d | \(2\) | \(0.138\) | \(\Q(\sqrt{-3}) \) | \(D_{6}\) | \(\Q(\sqrt{-23}) \) | None | \(1\) | \(-1\) | \(0\) | \(0\) | \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots\) |