# Properties

 Label 16.2.e Level $16$ Weight $2$ Character orbit 16.e Rep. character $\chi_{16}(5,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $4$ Trace bound $0$

# Related objects

## Defining parameters

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

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(16, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

## Trace form

 $$2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 4 q^{6} + 4 q^{8} + O(q^{10})$$ $$2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 2 q^{11} - 4 q^{12} - 2 q^{13} - 4 q^{14} + 4 q^{15} - 8 q^{16} - 4 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{26} - 8 q^{27} + 8 q^{28} + 6 q^{29} - 4 q^{30} - 16 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} + 6 q^{37} - 12 q^{38} - 8 q^{40} + 10 q^{43} - 4 q^{44} + 2 q^{45} + 12 q^{46} + 16 q^{47} + 8 q^{48} + 6 q^{49} - 6 q^{50} + 4 q^{51} - 4 q^{52} - 10 q^{53} - 8 q^{56} - 12 q^{58} - 6 q^{59} - 18 q^{61} + 16 q^{62} + 4 q^{63} + 4 q^{65} + 4 q^{66} - 10 q^{67} - 12 q^{69} + 8 q^{70} + 4 q^{72} + 6 q^{75} + 12 q^{76} + 4 q^{77} - 4 q^{78} + 8 q^{80} + 10 q^{81} - 2 q^{83} - 8 q^{84} + 4 q^{85} + 8 q^{88} - 4 q^{90} + 4 q^{91} - 24 q^{92} + 16 q^{93} - 16 q^{94} - 12 q^{95} - 16 q^{96} - 4 q^{97} - 6 q^{98} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(16, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.2.e.a $2$ $0.128$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$-2$$ $$-2$$ $$0$$ $$q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots$$