# Properties

 Label 187.2.p Level 187 Weight 2 Character orbit p Rep. character $$\chi_{187}(4,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 128 Newforms 1 Sturm bound 36 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$187 = 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 187.p (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$187$$ Character field: $$\Q(\zeta_{20})$$ Newforms: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 160 160 0
Cusp forms 128 128 0
Eisenstein series 32 32 0

## Trace form

 $$128q - 10q^{3} + 16q^{4} - 2q^{5} - 8q^{6} + O(q^{10})$$ $$128q - 10q^{3} + 16q^{4} - 2q^{5} - 8q^{6} - 24q^{10} - 40q^{13} + 2q^{14} - 48q^{16} - 18q^{17} - 2q^{20} + 16q^{21} - 70q^{22} - 16q^{23} + 28q^{24} - 22q^{27} + 42q^{28} - 2q^{29} - 44q^{30} - 6q^{31} + 32q^{33} + 44q^{34} + 12q^{35} + 30q^{37} - 80q^{38} + 78q^{39} - 100q^{40} - 56q^{41} + 52q^{44} - 68q^{45} + 14q^{46} - 16q^{47} - 110q^{48} + 84q^{50} + 14q^{51} - 100q^{52} - 20q^{54} - 84q^{55} + 36q^{56} - 48q^{57} - 26q^{58} + 28q^{61} + 108q^{62} - 40q^{63} + 120q^{64} + 28q^{65} - 48q^{67} + 102q^{68} + 24q^{69} + 2q^{71} + 80q^{72} - 30q^{73} - 28q^{74} - 80q^{75} - 104q^{78} + 44q^{79} - 92q^{80} + 140q^{81} - 28q^{82} - 52q^{84} + 76q^{85} + 12q^{86} + 50q^{88} - 32q^{89} + 204q^{90} + 42q^{91} + 2q^{92} + 16q^{95} + 240q^{96} - 34q^{97} + 24q^{98} - 90q^{99} + O(q^{100})$$

## 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.p.a $$128$$ $$1.493$$ None $$0$$ $$-10$$ $$-2$$ $$0$$