# Properties

 Label 91.2.h Level $91$ Weight $2$ Character orbit 91.h Rep. character $\chi_{91}(16,\cdot)$ 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.h (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

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

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