# Properties

 Label 89.2.a Level 89 Weight 2 Character orbit a Rep. character $$\chi_{89}(1,\cdot)$$ Character field $$\Q$$ Dimension 7 Newforms 3 Sturm bound 15 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$89$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 89.a (trivial) Character field: $$\Q$$ Newforms: $$3$$ Sturm bound: $$15$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(89))$$.

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 0
Eisenstein series 1 1 0

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

$$89$$Dim.
$$+$$$$1$$
$$-$$$$6$$

## Trace form

 $$7q - q^{2} - 2q^{3} + 9q^{4} - 4q^{5} + 6q^{7} + 3q^{8} + q^{9} + O(q^{10})$$ $$7q - q^{2} - 2q^{3} + 9q^{4} - 4q^{5} + 6q^{7} + 3q^{8} + q^{9} - 4q^{10} - 16q^{12} + 4q^{13} - 8q^{14} + 6q^{15} + 9q^{16} - 4q^{17} - 15q^{18} + 6q^{19} - 28q^{20} - 4q^{21} - 16q^{22} + 10q^{23} - 14q^{24} - q^{25} - 4q^{26} + 4q^{27} + 14q^{28} - 4q^{29} + 16q^{31} + 15q^{32} - 10q^{33} - 8q^{34} + 4q^{35} + 31q^{36} - 6q^{37} + 26q^{38} + 24q^{39} - 8q^{40} - 8q^{41} + 16q^{42} - 4q^{43} + 12q^{44} - 26q^{45} + 18q^{46} - 4q^{47} - 46q^{48} + 15q^{49} + 19q^{50} - 10q^{51} + 8q^{52} - 20q^{53} + 16q^{54} + 16q^{55} - 8q^{56} - 6q^{57} - 20q^{58} - 6q^{59} + 60q^{60} + 4q^{61} + 2q^{62} + 20q^{63} + 25q^{64} - 18q^{65} + 38q^{66} + 28q^{67} - 24q^{68} - 42q^{69} - 18q^{70} - 8q^{71} - 31q^{72} - 8q^{73} + 6q^{74} - 22q^{75} + 28q^{76} - 8q^{77} - 44q^{78} + 36q^{79} - 52q^{80} - 17q^{81} + 32q^{82} - 14q^{83} - 48q^{84} - 26q^{85} + 12q^{86} - 72q^{88} + 5q^{89} + 18q^{90} - 24q^{91} + 24q^{92} - 6q^{93} - 4q^{94} + 14q^{95} + 8q^{96} + 4q^{97} - 41q^{98} + 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(89))$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 89
89.2.a.a $$1$$ $$0.711$$ $$\Q$$ None $$-1$$ $$-1$$ $$-1$$ $$-4$$ $$+$$ $$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$$
89.2.a.b $$1$$ $$0.711$$ $$\Q$$ None $$1$$ $$2$$ $$-2$$ $$2$$ $$-$$ $$q+q^{2}+2q^{3}-q^{4}-2q^{5}+2q^{6}+2q^{7}+\cdots$$
89.2.a.c $$5$$ $$0.711$$ 5.5.535120.1 None $$-1$$ $$-3$$ $$-1$$ $$8$$ $$-$$ $$q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(3-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$$