# Properties

 Label 91.2.a Level $91$ Weight $2$ Character orbit 91.a Rep. character $\chi_{91}(1,\cdot)$ Character field $\Q$ Dimension $7$ Newform subspaces $4$ Sturm bound $18$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$91 = 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 91.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$18$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(91))$$.

Total New Old
Modular forms 10 7 3
Cusp forms 7 7 0
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$7$$$$13$$FrickeDim
$$+$$$$+$$$+$$$1$$
$$+$$$$-$$$-$$$3$$
$$-$$$$+$$$-$$$2$$
$$-$$$$-$$$+$$$1$$
Plus space$$+$$$$2$$
Minus space$$-$$$$5$$

## Trace form

 $$7 q - q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - q^{7} + 3 q^{8} + 3 q^{9} + O(q^{10})$$ $$7 q - q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} - 4 q^{11} - 8 q^{12} + q^{13} + q^{14} - 4 q^{15} - 9 q^{16} + 2 q^{17} - 9 q^{18} - 12 q^{19} - 2 q^{20} - 4 q^{22} + 10 q^{23} - 4 q^{24} + 15 q^{25} + 3 q^{26} - 4 q^{27} - 7 q^{28} + 16 q^{29} + 8 q^{30} - 4 q^{31} + 15 q^{32} - 4 q^{33} + 2 q^{34} + 4 q^{35} - 9 q^{36} - 6 q^{37} - 8 q^{38} - 4 q^{39} - 10 q^{40} + 2 q^{41} - 8 q^{42} - 2 q^{43} + 22 q^{45} - 16 q^{46} + 8 q^{47} + 12 q^{48} + 7 q^{49} + q^{50} + 8 q^{51} - q^{52} - 16 q^{53} + 48 q^{54} + 12 q^{55} - 3 q^{56} + 30 q^{58} + 16 q^{59} - 20 q^{60} - 14 q^{61} - 8 q^{62} - 5 q^{63} - 17 q^{64} - 4 q^{65} + 12 q^{66} - 16 q^{67} + 42 q^{68} - 20 q^{69} + 6 q^{70} - 32 q^{71} - q^{72} - 22 q^{73} + 26 q^{74} - 48 q^{75} + 16 q^{76} + 4 q^{77} + 8 q^{78} + 2 q^{79} - 38 q^{80} - 9 q^{81} + 14 q^{82} + 24 q^{83} + 16 q^{84} - 8 q^{85} - 24 q^{86} - 16 q^{87} + 36 q^{88} + 26 q^{89} - 50 q^{90} - 3 q^{91} - 12 q^{92} - 20 q^{93} - 20 q^{94} + 6 q^{95} - 4 q^{96} - 6 q^{97} - q^{98} + 32 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(91))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 13
91.2.a.a $1$ $0.727$ $$\Q$$ None $$-2$$ $$0$$ $$-3$$ $$-1$$ $+$ $+$ $$q-2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots$$
91.2.a.b $1$ $0.727$ $$\Q$$ None $$0$$ $$-2$$ $$-3$$ $$1$$ $-$ $-$ $$q-2q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots$$
91.2.a.c $2$ $0.727$ $$\Q(\sqrt{2})$$ None $$0$$ $$0$$ $$6$$ $$2$$ $-$ $+$ $$q+\beta q^{2}-\beta q^{3}+(3+\beta )q^{5}-2q^{6}+q^{7}+\cdots$$
91.2.a.d $3$ $0.727$ 3.3.316.1 None $$1$$ $$-2$$ $$2$$ $$-3$$ $+$ $-$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$$