# Properties

 Label 55.2.j Level 55 Weight 2 Character orbit j Rep. character $$\chi_{55}(4,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 16 Newforms 1 Sturm bound 12 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$55 = 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 55.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$55$$ Character field: $$\Q(\zeta_{10})$$ Newforms: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(55, [\chi])$$.

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

## Trace form

 $$16q - 4q^{4} - 2q^{5} - 18q^{6} + 2q^{9} + O(q^{10})$$ $$16q - 4q^{4} - 2q^{5} - 18q^{6} + 2q^{9} - 6q^{11} - 12q^{14} - 16q^{15} + 16q^{16} + 6q^{19} - 8q^{20} + 8q^{21} + 6q^{24} - 16q^{25} + 40q^{26} + 2q^{29} + 26q^{30} + 8q^{31} - 16q^{34} + 22q^{35} + 10q^{36} + 30q^{39} + 12q^{40} - 52q^{41} + 4q^{44} + 12q^{45} - 62q^{46} - 10q^{49} + 28q^{50} - 42q^{51} - 40q^{54} - 8q^{55} - 20q^{56} + 2q^{59} - 32q^{60} - 40q^{61} - 8q^{64} - 40q^{65} + 58q^{66} + 26q^{69} - 34q^{70} + 36q^{71} + 48q^{74} - 20q^{75} + 56q^{76} + 38q^{79} + 34q^{80} + 68q^{81} + 12q^{84} + 58q^{85} + 22q^{86} + 24q^{89} + 78q^{90} - 20q^{91} + 14q^{94} + 48q^{95} - 86q^{96} - 72q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(55, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
55.2.j.a $$16$$ $$0.439$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots$$