# Properties

 Label 185.2.f Level $185$ Weight $2$ Character orbit 185.f Rep. character $\chi_{185}(43,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $34$ Newform subspaces $4$ Sturm bound $38$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$185 = 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 185.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$185$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$38$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(185, [\chi])$$.

Total New Old
Modular forms 42 42 0
Cusp forms 34 34 0
Eisenstein series 8 8 0

## Trace form

 $$34q + 4q^{3} - 30q^{4} - 6q^{5} - 4q^{6} - 4q^{7} + O(q^{10})$$ $$34q + 4q^{3} - 30q^{4} - 6q^{5} - 4q^{6} - 4q^{7} - 6q^{10} - 32q^{12} + 12q^{14} + 10q^{15} + 14q^{16} - 20q^{17} - 22q^{18} + 4q^{19} - 8q^{20} + 20q^{22} + 36q^{24} + 10q^{25} - 20q^{27} - 8q^{28} + 14q^{29} - 8q^{30} + 8q^{33} - 26q^{35} - 12q^{37} - 60q^{38} + 4q^{39} + 18q^{40} + 64q^{42} + 30q^{45} + 40q^{46} + 12q^{47} + 60q^{48} + 24q^{50} - 4q^{51} - 10q^{53} + 40q^{54} + 18q^{55} - 28q^{56} - 22q^{58} - 8q^{59} - 104q^{60} - 10q^{61} - 32q^{62} + 36q^{63} - 38q^{64} + 32q^{65} + 16q^{66} + 8q^{67} + 8q^{68} - 40q^{69} - 20q^{70} + 8q^{71} + 70q^{72} + 30q^{73} + 34q^{74} + 20q^{75} - 36q^{77} - 36q^{78} - 40q^{79} - 8q^{80} - 18q^{81} - 4q^{82} - 24q^{83} - 20q^{85} + 88q^{86} - 64q^{87} - 24q^{88} - 34q^{89} - 4q^{90} + 52q^{91} + 52q^{94} + 20q^{95} - 88q^{96} + 56q^{97} - 102q^{98} - 64q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(185, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
185.2.f.a $$2$$ $$1.477$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-4$$ $$-6$$ $$q-iq^{2}+(-1-i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots$$
185.2.f.b $$2$$ $$1.477$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$-4$$ $$0$$ $$q-iq^{2}+(2+2i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots$$
185.2.f.c $$6$$ $$1.477$$ 6.0.350464.1 None $$0$$ $$-2$$ $$2$$ $$-4$$ $$q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots$$
185.2.f.d $$24$$ $$1.477$$ None $$0$$ $$4$$ $$0$$ $$6$$