# Properties

 Label 187.2.e Level 187 Weight 2 Character orbit e Rep. character $$\chi_{187}(89,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 32 Newforms 2 Sturm bound 36 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$187 = 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 187.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$17$$ Character field: $$\Q(i)$$ Newforms: $$2$$ Sturm bound: $$36$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(187, [\chi])$$.

Total New Old
Modular forms 40 32 8
Cusp forms 32 32 0
Eisenstein series 8 0 8

## Trace form

 $$32q - 36q^{4} - 8q^{5} + 8q^{6} + O(q^{10})$$ $$32q - 36q^{4} - 8q^{5} + 8q^{6} + 4q^{10} - 20q^{12} - 12q^{14} + 28q^{16} - 12q^{17} - 20q^{18} + 12q^{20} + 24q^{21} - 4q^{23} + 12q^{24} + 12q^{27} - 52q^{28} + 12q^{29} + 24q^{30} - 24q^{31} + 8q^{33} + 16q^{34} - 32q^{35} - 20q^{37} - 40q^{38} - 8q^{39} - 20q^{40} + 16q^{41} + 8q^{44} + 48q^{45} + 36q^{46} - 4q^{47} + 60q^{48} + 36q^{50} + 56q^{51} - 16q^{55} + 64q^{56} - 32q^{57} - 64q^{58} - 8q^{61} + 52q^{62} + 20q^{63} + 20q^{64} - 48q^{65} - 12q^{67} - 32q^{68} - 64q^{69} + 28q^{71} + 20q^{72} + 20q^{73} + 68q^{74} + 4q^{78} + 16q^{79} - 48q^{80} - 80q^{81} - 12q^{82} - 168q^{84} + 24q^{85} + 8q^{86} + 12q^{89} - 104q^{90} + 8q^{91} + 68q^{92} - 36q^{95} - 140q^{96} - 16q^{97} + 116q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(187, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
187.2.e.a $$4$$ $$1.493$$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$8$$ $$0$$ $$q+2\zeta_{8}^{2}q^{2}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots$$
187.2.e.b $$28$$ $$1.493$$ None $$0$$ $$4$$ $$-16$$ $$0$$