# Properties

 Label 91.2.k Level $91$ Weight $2$ Character orbit 91.k Rep. character $\chi_{91}(4,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $14$ Newform subspaces $2$ Sturm bound $18$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$91 = 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 91.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(91, [\chi])$$.

Total New Old
Modular forms 22 22 0
Cusp forms 14 14 0
Eisenstein series 8 8 0

## Trace form

 $$14 q - 2 q^{3} - 10 q^{4} - 6 q^{6} - 7 q^{7} + q^{9} + O(q^{10})$$ $$14 q - 2 q^{3} - 10 q^{4} - 6 q^{6} - 7 q^{7} + q^{9} + 9 q^{10} + 3 q^{11} - 2 q^{12} - 4 q^{13} + 10 q^{14} - 9 q^{15} + 6 q^{16} - 22 q^{17} - 3 q^{18} + 6 q^{19} - 6 q^{20} + 16 q^{21} - 6 q^{22} - 6 q^{23} + 18 q^{24} - 7 q^{25} + 6 q^{26} + 22 q^{27} - 5 q^{28} - 4 q^{29} + 14 q^{30} + 15 q^{31} - 15 q^{33} - 9 q^{35} - 15 q^{36} + 16 q^{38} - 11 q^{39} - 4 q^{40} - 15 q^{41} - 11 q^{42} - 24 q^{44} + 14 q^{48} - q^{49} + 24 q^{50} + 10 q^{51} - 5 q^{52} + q^{53} - 24 q^{55} + 33 q^{56} - 15 q^{58} - 33 q^{60} - 2 q^{61} + 38 q^{62} - 28 q^{63} + 24 q^{65} - 43 q^{66} + 30 q^{67} + 10 q^{68} + 7 q^{69} + 18 q^{70} + 33 q^{71} + 51 q^{72} + 57 q^{73} + 66 q^{74} - 6 q^{75} - 42 q^{76} - 10 q^{77} + 47 q^{78} - 30 q^{79} - 78 q^{80} + 13 q^{81} - 4 q^{82} - 7 q^{84} - 3 q^{85} - 90 q^{86} - 26 q^{87} - 5 q^{88} - 12 q^{90} - 15 q^{91} - 66 q^{92} - 14 q^{94} - 10 q^{95} + 12 q^{96} - 12 q^{97} - 42 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(91, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.2.k.a $2$ $0.727$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$3$$ $$-4$$ $$q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(2-\zeta_{6})q^{5}+\cdots$$
91.2.k.b $12$ $0.727$ 12.0.$$\cdots$$.1 None $$0$$ $$-3$$ $$-3$$ $$-3$$ $$q+\beta _{9}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots$$