# Properties

 Label 61.2.a Level 61 Weight 2 Character orbit a Rep. character $$\chi_{61}(1,\cdot)$$ Character field $$\Q$$ Dimension 4 Newforms 2 Sturm bound 10 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$61$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 61.a (trivial) Character field: $$\Q$$ Newforms: $$2$$ Sturm bound: $$10$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(61))$$.

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 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.

$$61$$Dim.
$$+$$$$1$$
$$-$$$$3$$

## Trace form

 $$4q - 4q^{5} - 2q^{6} - 2q^{7} + 6q^{8} + 4q^{9} + O(q^{10})$$ $$4q - 4q^{5} - 2q^{6} - 2q^{7} + 6q^{8} + 4q^{9} - 6q^{10} + 8q^{11} - 8q^{12} - 8q^{13} - 4q^{14} + 4q^{15} - 4q^{16} + 2q^{17} + 4q^{18} - 4q^{19} + 4q^{20} - 10q^{21} + 16q^{22} - 4q^{23} - 10q^{24} + 8q^{25} + 12q^{27} + 4q^{28} - 2q^{29} - 6q^{30} - 2q^{31} - 8q^{32} + 14q^{33} + 4q^{34} + 8q^{35} - 12q^{36} + 2q^{37} + 18q^{38} + 4q^{39} + 8q^{41} - 22q^{43} + 14q^{44} - 24q^{45} + 4q^{46} + 12q^{48} - 16q^{49} - 16q^{50} - 8q^{51} - 16q^{52} + 4q^{53} + 16q^{54} + 2q^{55} + 8q^{56} - 24q^{57} + 16q^{58} + 38q^{59} + 16q^{60} + 2q^{61} - 32q^{62} - 18q^{63} - 4q^{64} - 20q^{65} - 32q^{66} + 2q^{67} - 6q^{68} + 26q^{69} + 4q^{70} + 6q^{71} - 10q^{72} - 12q^{73} + 4q^{74} + 4q^{75} + 36q^{76} - 20q^{77} + 26q^{78} + 16q^{79} - 16q^{80} - 12q^{81} - 12q^{82} - 4q^{83} + 22q^{84} - 30q^{85} + 12q^{86} + 16q^{87} - 4q^{88} - 8q^{89} + 10q^{90} - 6q^{91} + 6q^{92} + 28q^{93} + 16q^{94} + 16q^{95} + 34q^{96} - 4q^{97} + 2q^{98} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(61))$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 61
61.2.a.a $$1$$ $$0.487$$ $$\Q$$ None $$-1$$ $$-2$$ $$-3$$ $$1$$ $$+$$ $$q-q^{2}-2q^{3}-q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots$$
61.2.a.b $$3$$ $$0.487$$ 3.3.148.1 None $$1$$ $$2$$ $$-1$$ $$-3$$ $$-$$ $$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$$