# Properties

 Label 6047.2.a Level 6047 Weight 2 Character orbit a Rep. character $$\chi_{6047}(1,\cdot)$$ Character field $$\Q$$ Dimension 504 Newform subspaces 2 Sturm bound 1008 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$6047$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6047.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$1008$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(6047))$$.

Total New Old
Modular forms 505 505 0
Cusp forms 504 504 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.

$$6047$$Dim.
$$+$$$$217$$
$$-$$$$287$$

## Trace form

 $$504q + q^{2} + 2q^{3} + 503q^{4} - 2q^{6} + 4q^{7} + 3q^{8} + 504q^{9} + O(q^{10})$$ $$504q + q^{2} + 2q^{3} + 503q^{4} - 2q^{6} + 4q^{7} + 3q^{8} + 504q^{9} - 8q^{10} + 8q^{12} + 6q^{13} - 8q^{14} - 2q^{15} + 497q^{16} - 2q^{17} + 5q^{18} - 4q^{19} - 14q^{20} - 10q^{21} + 6q^{22} + 8q^{23} - 10q^{24} + 518q^{25} + 10q^{26} + 14q^{27} + 16q^{28} - 8q^{29} - 24q^{30} + 4q^{31} + 17q^{32} + 6q^{33} - 4q^{34} - 42q^{35} + 485q^{36} + 34q^{37} - 16q^{38} - 10q^{39} - 20q^{40} + 18q^{41} - 32q^{42} - 2q^{43} + 26q^{44} + 4q^{45} - 14q^{46} + 12q^{47} + 26q^{48} + 506q^{49} + 43q^{50} + 8q^{51} + 6q^{52} - 8q^{53} - 16q^{55} - 28q^{56} + 42q^{57} + 58q^{58} - 6q^{59} - 54q^{60} - 2q^{61} + 8q^{62} - 12q^{63} + 519q^{64} + 4q^{65} - 22q^{66} + 26q^{67} + 26q^{68} + 2q^{69} - 2q^{70} - 32q^{71} + 15q^{72} + 46q^{73} + 16q^{74} - 14q^{75} - 2q^{76} - 14q^{77} + 68q^{78} + 26q^{79} - 22q^{80} + 520q^{81} + 2q^{82} + 26q^{83} + 22q^{84} + 12q^{85} + 54q^{86} - 14q^{87} + 4q^{88} + 10q^{89} + 14q^{92} + 34q^{93} - 40q^{94} - 8q^{95} - 10q^{96} + 56q^{97} + 45q^{98} + 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(6047))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 6047
6047.2.a.a $$217$$ $$48.286$$ None $$-20$$ $$-27$$ $$-19$$ $$-48$$ $$+$$
6047.2.a.b $$287$$ $$48.286$$ None $$21$$ $$29$$ $$19$$ $$52$$ $$-$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database