# Properties

 Label 91.2.f Level $91$ Weight $2$ Character orbit 91.f Rep. character $\chi_{91}(22,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $3$ Sturm bound $18$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$91 = 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 91.f (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$18$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 24 16 8
Cusp forms 16 16 0
Eisenstein series 8 0 8

## Trace form

 $$16 q - 2 q^{2} - 10 q^{4} - 8 q^{5} + 6 q^{6} - 10 q^{9} + O(q^{10})$$ $$16 q - 2 q^{2} - 10 q^{4} - 8 q^{5} + 6 q^{6} - 10 q^{9} - 2 q^{10} - 2 q^{11} + 4 q^{12} - 2 q^{13} + 8 q^{14} - 2 q^{15} - 22 q^{16} + 10 q^{17} + 36 q^{18} - 8 q^{19} - 10 q^{20} - 4 q^{21} - 2 q^{22} - 4 q^{23} + 28 q^{24} - 4 q^{25} - 12 q^{26} - 36 q^{27} + 2 q^{29} + 16 q^{30} - 4 q^{31} + 18 q^{32} + 22 q^{33} - 8 q^{34} - 10 q^{35} + 8 q^{36} + 16 q^{37} - 52 q^{38} + 12 q^{39} - 8 q^{40} + 16 q^{41} - 4 q^{42} - 18 q^{43} + 24 q^{44} - 10 q^{45} - 20 q^{46} + 28 q^{47} + 26 q^{48} - 8 q^{49} - 46 q^{50} - 20 q^{51} + 78 q^{52} + 16 q^{53} + 6 q^{55} - 12 q^{56} - 20 q^{57} - 6 q^{58} - 10 q^{59} - 76 q^{60} + 24 q^{61} - 4 q^{62} + 4 q^{63} + 40 q^{64} + 10 q^{65} + 12 q^{66} + 20 q^{67} + 66 q^{68} - 4 q^{69} + 48 q^{70} + 8 q^{71} - 26 q^{72} - 16 q^{73} - 32 q^{74} + 14 q^{75} - 18 q^{76} + 8 q^{77} - 74 q^{78} + 8 q^{79} - 34 q^{80} - 28 q^{81} + 28 q^{82} + 12 q^{83} + 22 q^{84} + 2 q^{85} + 48 q^{86} + 10 q^{87} - 30 q^{88} - 32 q^{89} + 116 q^{90} + 2 q^{91} - 24 q^{92} - 18 q^{93} - 52 q^{94} - 18 q^{95} - 212 q^{96} - 26 q^{97} - 2 q^{98} + 76 q^{99} + O(q^{100})$$

## 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.f.a $4$ $0.727$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$-3$$ $$3$$ $$6$$ $$-2$$ $$q+(-1-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots$$
91.2.f.b $4$ $0.727$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$-2$$ $$q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$$
91.2.f.c $8$ $0.727$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$1$$ $$-1$$ $$-14$$ $$4$$ $$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$