# Properties

 Label 16.3.f Level $16$ Weight $3$ Character orbit 16.f Rep. character $\chi_{16}(3,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$16 = 2^{4}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 16.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(16, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

## Trace form

 $$6q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} - 8q^{6} - 4q^{7} + 4q^{8} + O(q^{10})$$ $$6q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} - 8q^{6} - 4q^{7} + 4q^{8} + 36q^{10} - 18q^{11} + 52q^{12} - 2q^{13} + 12q^{14} - 40q^{16} - 4q^{17} - 74q^{18} + 30q^{19} - 84q^{20} - 20q^{21} - 52q^{22} + 60q^{23} + 48q^{24} + 96q^{26} + 64q^{27} + 56q^{28} - 18q^{29} + 52q^{30} + 8q^{32} - 4q^{33} - 76q^{34} - 100q^{35} - 52q^{36} + 46q^{37} + 40q^{38} - 196q^{39} + 40q^{40} - 24q^{42} - 114q^{43} + 20q^{44} + 66q^{45} + 28q^{46} - 24q^{48} - 46q^{49} + 46q^{50} + 156q^{51} + 100q^{52} + 78q^{53} + 32q^{54} + 252q^{55} - 168q^{56} - 176q^{58} + 206q^{59} - 160q^{60} + 30q^{61} - 144q^{62} + 64q^{64} + 12q^{65} + 196q^{66} - 226q^{67} + 112q^{68} - 116q^{69} - 16q^{70} - 260q^{71} + 52q^{72} - 92q^{74} - 238q^{75} - 188q^{76} - 212q^{77} - 84q^{78} + 232q^{80} + 86q^{81} + 304q^{82} + 318q^{83} + 232q^{84} - 212q^{85} + 268q^{86} + 444q^{87} - 8q^{88} - 160q^{90} + 188q^{91} - 168q^{92} - 32q^{93} + 48q^{94} - 80q^{96} - 4q^{97} + 10q^{98} - 226q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(16, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
16.3.f.a $$6$$ $$0.436$$ 6.0.399424.1 None $$-2$$ $$-2$$ $$-2$$ $$-4$$ $$q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$$