# Properties

 Label 6037.2.a Level 6037 Weight 2 Character orbit a Rep. character $$\chi_{6037}(1,\cdot)$$ Character field $$\Q$$ Dimension 502 Newform subspaces 2 Sturm bound 1006 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$6037$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6037.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$1006$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(6037))$$.

Total New Old
Modular forms 503 503 0
Cusp forms 502 502 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 and the Fricke involution.

$$6037$$Dim.
$$+$$$$243$$
$$-$$$$259$$

## Trace form

 $$502q - 2q^{3} + 502q^{4} - 2q^{5} + 6q^{6} + 6q^{8} + 500q^{9} + O(q^{10})$$ $$502q - 2q^{3} + 502q^{4} - 2q^{5} + 6q^{6} + 6q^{8} + 500q^{9} + 4q^{10} - 4q^{11} - 8q^{12} - 12q^{13} - 16q^{15} + 514q^{16} - 4q^{17} - 18q^{18} - 4q^{20} - 12q^{21} + 18q^{22} - 12q^{24} + 494q^{25} - 14q^{26} - 14q^{27} + 2q^{29} - 16q^{30} - 10q^{31} + 12q^{32} - 10q^{33} - 12q^{35} + 510q^{36} - 12q^{37} - 12q^{38} - 30q^{39} + 28q^{40} - 14q^{41} - 32q^{42} - 38q^{44} - 40q^{45} + 32q^{46} - 6q^{47} + 2q^{48} + 484q^{49} + 16q^{50} - 30q^{51} - 12q^{52} - 10q^{53} + 24q^{54} + 10q^{55} + 24q^{56} + 6q^{57} + 26q^{58} + 16q^{59} - 26q^{60} + 6q^{61} - 26q^{62} - 50q^{63} + 562q^{64} - 46q^{65} + 10q^{66} + 6q^{67} - 10q^{68} - 24q^{69} + 114q^{70} - 20q^{71} - 16q^{72} + 18q^{73} + 16q^{74} - 52q^{75} + 28q^{76} + 6q^{78} + 4q^{79} - 42q^{80} + 486q^{81} + 16q^{82} - 52q^{84} + 18q^{85} + 56q^{86} - 40q^{87} + 96q^{88} + 16q^{89} - 32q^{90} - 46q^{91} + 42q^{92} - 4q^{93} + 76q^{94} - 28q^{95} - 6q^{96} + 14q^{97} - 72q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(6037))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 6037
6037.2.a.a $$243$$ $$48.206$$ None $$-47$$ $$-31$$ $$-40$$ $$-42$$ $$+$$
6037.2.a.b $$259$$ $$48.206$$ None $$47$$ $$29$$ $$38$$ $$42$$ $$-$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database