# Properties

 Label 91.2.g Level $91$ Weight $2$ Character orbit 91.g Rep. character $\chi_{91}(9,\cdot)$ Character field $\Q(\zeta_{3})$ 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.g (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{3})$$ 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

 $$14 q + q^{2} - 8 q^{3} - 3 q^{4} - 2 q^{5} - 6 q^{6} + 4 q^{7} - 12 q^{8} + 6 q^{9} + O(q^{10})$$ $$14 q + q^{2} - 8 q^{3} - 3 q^{4} - 2 q^{5} - 6 q^{6} + 4 q^{7} - 12 q^{8} + 6 q^{9} - 2 q^{10} - 14 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 7 q^{15} + 9 q^{16} + 7 q^{17} - 3 q^{18} + 2 q^{20} + 6 q^{21} - 2 q^{22} - q^{23} + 40 q^{24} + 3 q^{25} - 26 q^{27} - 8 q^{28} - 4 q^{29} - 8 q^{30} + 13 q^{31} + 3 q^{32} - 14 q^{33} + 28 q^{34} + 11 q^{35} - 15 q^{36} - 15 q^{37} - 16 q^{38} - 17 q^{39} + 4 q^{40} - 11 q^{41} - 10 q^{42} - 4 q^{43} + 18 q^{44} - 25 q^{45} + 16 q^{46} - 2 q^{47} + 18 q^{48} + 8 q^{49} + 2 q^{50} - 26 q^{51} - 32 q^{52} - 5 q^{53} - 9 q^{54} + 18 q^{55} - 3 q^{56} + 48 q^{57} + 30 q^{58} + 17 q^{59} + 11 q^{60} - 16 q^{61} + 2 q^{62} + 2 q^{63} - 16 q^{64} + 40 q^{65} + 9 q^{66} + 16 q^{67} + 27 q^{68} + 23 q^{69} - 54 q^{70} - 7 q^{71} - 86 q^{72} - 17 q^{73} - 5 q^{74} + 9 q^{75} - 10 q^{76} + 26 q^{77} + 31 q^{78} + 10 q^{79} + 8 q^{80} + 30 q^{81} + 4 q^{82} - 54 q^{83} + 8 q^{84} + 5 q^{85} + 37 q^{87} + 18 q^{88} - 2 q^{89} + 20 q^{90} - 9 q^{91} + 54 q^{92} + 2 q^{93} - 88 q^{94} - 3 q^{95} + 34 q^{96} - 30 q^{97} + 49 q^{98} - 56 q^{99} + O(q^{100})$$

## 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.g.a $$2$$ $$0.727$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-6$$ $$-3$$ $$-5$$ $$q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}+(-3+\cdots)q^{5}+\cdots$$
91.2.g.b $$12$$ $$0.727$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$2$$ $$-2$$ $$1$$ $$9$$ $$q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+(\beta _{3}-\beta _{11})q^{3}+\cdots$$