# Properties

 Label 55.2.g Level 55 Weight 2 Character orbit g Rep. character $$\chi_{55}(16,\cdot)$$ Character field $$\Q(\zeta_{5})$$ Dimension 16 Newforms 2 Sturm bound 12 Trace bound 2

# Related objects

## Defining parameters

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

## Dimensions

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

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

## Trace form

 $$16q - 6q^{2} - 4q^{3} - 8q^{4} + 6q^{6} - 4q^{7} + 2q^{8} - 10q^{9} + O(q^{10})$$ $$16q - 6q^{2} - 4q^{3} - 8q^{4} + 6q^{6} - 4q^{7} + 2q^{8} - 10q^{9} + 8q^{10} - 2q^{11} - 12q^{12} + 2q^{13} + 6q^{15} - 16q^{16} - 12q^{17} + 14q^{18} + 14q^{19} - 4q^{20} - 32q^{21} + 26q^{22} - 8q^{23} + 38q^{24} - 4q^{25} - 4q^{26} + 20q^{27} - 2q^{28} + 10q^{29} - 20q^{30} - 4q^{31} + 28q^{32} - 14q^{33} - 16q^{34} - 12q^{35} + 6q^{36} + 28q^{37} - 6q^{38} + 30q^{39} - 6q^{40} + 4q^{41} + 38q^{42} + 4q^{43} - 40q^{44} - 38q^{46} + 4q^{47} - 14q^{48} - 14q^{49} - 6q^{50} + 14q^{51} - 54q^{52} + 16q^{53} - 24q^{54} + 12q^{55} + 52q^{56} - 50q^{57} + 6q^{58} - 46q^{59} + 26q^{60} + 4q^{61} - 68q^{62} + 26q^{63} - 20q^{64} + 16q^{65} + 26q^{66} - 40q^{67} + 46q^{68} - 22q^{69} + 32q^{70} + 20q^{71} - 64q^{72} - 10q^{73} + 68q^{74} + 6q^{75} + 16q^{76} + 6q^{77} - 4q^{78} + 54q^{79} + 16q^{80} + 8q^{81} + 30q^{82} + 2q^{83} + 24q^{84} - 16q^{85} - 34q^{86} + 68q^{87} - 14q^{88} - 16q^{89} - 26q^{90} + 32q^{91} + 92q^{92} - 48q^{93} + 50q^{94} - 16q^{95} + 6q^{96} + 36q^{97} - 68q^{98} - 16q^{99} + O(q^{100})$$

## 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.g.a $$8$$ $$0.439$$ 8.0.159390625.1 None $$-4$$ $$1$$ $$-2$$ $$-3$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$$
55.2.g.b $$8$$ $$0.439$$ 8.0.13140625.1 None $$-2$$ $$-5$$ $$2$$ $$-1$$ $$q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$$