# Properties

 Label 187.2.t Level 187 Weight 2 Character orbit t Rep. character $$\chi_{187}(6,\cdot)$$ Character field $$\Q(\zeta_{80})$$ Dimension 512 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.t (of order $$80$$ and degree $$32$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$187$$ Character field: $$\Q(\zeta_{80})$$ 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 640 640 0
Cusp forms 512 512 0
Eisenstein series 128 128 0

## Trace form

 $$512q - 40q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 40q^{6} - 40q^{7} - 40q^{8} - 24q^{9} + O(q^{10})$$ $$512q - 40q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 40q^{6} - 40q^{7} - 40q^{8} - 24q^{9} - 40q^{11} - 16q^{12} - 56q^{14} - 24q^{15} - 40q^{17} - 80q^{18} - 40q^{19} - 24q^{20} - 48q^{22} - 48q^{23} + 80q^{24} - 40q^{25} - 56q^{26} + 48q^{27} - 40q^{28} - 40q^{29} - 40q^{30} + 40q^{31} - 64q^{34} - 80q^{35} - 56q^{36} - 56q^{37} + 80q^{38} - 40q^{39} - 40q^{40} + 80q^{41} + 72q^{42} + 32q^{44} - 64q^{45} - 40q^{46} - 24q^{47} - 72q^{48} - 88q^{49} - 40q^{51} + 240q^{52} - 24q^{53} + 128q^{55} - 64q^{56} - 40q^{57} + 88q^{58} - 88q^{59} - 152q^{60} - 40q^{61} - 40q^{62} + 80q^{63} - 88q^{64} + 408q^{66} - 40q^{68} + 192q^{69} - 168q^{70} - 24q^{71} - 40q^{72} - 40q^{73} - 40q^{74} - 88q^{75} + 192q^{77} - 64q^{78} - 40q^{79} + 248q^{80} - 40q^{81} - 24q^{82} - 40q^{85} - 112q^{86} + 128q^{88} - 64q^{89} - 40q^{90} + 56q^{91} + 136q^{92} - 88q^{93} + 440q^{94} - 40q^{95} - 40q^{96} - 88q^{97} + 72q^{99} + O(q^{100})$$

## 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.t.a $$512$$ $$1.493$$ None $$-40$$ $$-24$$ $$-24$$ $$-40$$