# Properties

 Label 91.2.e Level $91$ Weight $2$ Character orbit 91.e Rep. character $\chi_{91}(53,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $3$ Sturm bound $18$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$91 = 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 91.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ 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 24 16 8
Cusp forms 16 16 0
Eisenstein series 8 0 8

## Trace form

 $$16 q - 2 q^{2} - 10 q^{4} - 2 q^{5} - 6 q^{7} - 4 q^{9} + O(q^{10})$$ $$16 q - 2 q^{2} - 10 q^{4} - 2 q^{5} - 6 q^{7} - 4 q^{9} + 10 q^{10} - 2 q^{11} + 10 q^{12} + 4 q^{13} - 10 q^{14} - 20 q^{15} - 22 q^{16} + 4 q^{17} - 8 q^{19} + 32 q^{20} + 2 q^{21} + 28 q^{22} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 30 q^{28} - 16 q^{29} - 2 q^{30} - 4 q^{31} - 12 q^{32} - 8 q^{33} - 32 q^{34} - 4 q^{35} + 32 q^{36} - 8 q^{37} + 26 q^{38} - 8 q^{40} + 28 q^{41} + 32 q^{42} - 24 q^{43} + 6 q^{44} + 32 q^{45} - 20 q^{46} - 2 q^{47} - 76 q^{48} - 20 q^{49} + 8 q^{50} + 28 q^{51} - 6 q^{52} - 8 q^{53} - 18 q^{54} - 32 q^{57} + 42 q^{58} - 10 q^{59} + 44 q^{60} + 12 q^{61} - 76 q^{62} + 40 q^{63} + 40 q^{64} - 2 q^{65} - 6 q^{66} - 4 q^{67} + 18 q^{68} + 56 q^{69} + 54 q^{70} + 20 q^{71} + 22 q^{72} - 22 q^{73} + 34 q^{74} + 20 q^{75} + 48 q^{76} - 52 q^{77} - 20 q^{78} - 4 q^{79} - 70 q^{80} + 32 q^{81} - 44 q^{82} + 12 q^{83} - 98 q^{84} - 4 q^{85} - 54 q^{86} + 28 q^{87} - 24 q^{88} + 4 q^{89} - 88 q^{90} + 8 q^{91} - 12 q^{92} - 18 q^{93} - 46 q^{94} + 12 q^{95} + 22 q^{96} - 68 q^{97} + 34 q^{98} + 16 q^{99} + O(q^{100})$$

## 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.e.a $2$ $0.727$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$1$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots$$
91.2.e.b $4$ $0.727$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$3$$ $$0$$ $$0$$ $$-8$$ $$q+(1+\beta _{1}+\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots$$
91.2.e.c $10$ $0.727$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-4$$ $$0$$ $$-2$$ $$1$$ $$q+(\beta _{1}-\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots$$