# Properties

 Label 68.2.i Level $68$ Weight $2$ Character orbit 68.i Rep. character $\chi_{68}(3,\cdot)$ Character field $\Q(\zeta_{16})$ Dimension $56$ Newform subspaces $2$ Sturm bound $18$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$68 = 2^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 68.i (of order $$16$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$68$$ Character field: $$\Q(\zeta_{16})$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(68, [\chi])$$.

Total New Old
Modular forms 88 88 0
Cusp forms 56 56 0
Eisenstein series 32 32 0

## Trace form

 $$56 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + O(q^{10})$$ $$56 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} - 16 q^{25} + 24 q^{26} + 40 q^{28} - 16 q^{29} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 16 q^{41} + 40 q^{42} + 24 q^{44} - 16 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} - 8 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 88 q^{65} - 96 q^{66} - 96 q^{68} + 32 q^{69} - 80 q^{70} - 112 q^{72} + 88 q^{73} - 56 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 48 q^{82} - 8 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 72 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 128 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(68, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
68.2.i.a $8$ $0.543$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{16}+\zeta_{16}^{5})q^{2}-2\zeta_{16}^{6}q^{4}+\cdots$$
68.2.i.b $48$ $0.543$ None $$-8$$ $$0$$ $$-16$$ $$0$$