# Properties

 Label 4019.2.a Level 4019 Weight 2 Character orbit a Rep. character $$\chi_{4019}(1,\cdot)$$ Character field $$\Q$$ Dimension 335 Newform subspaces 2 Sturm bound 670 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$4019$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4019.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$670$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(4019))$$.

Total New Old
Modular forms 336 336 0
Cusp forms 335 335 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.

$$4019$$Dim.
$$+$$$$149$$
$$-$$$$186$$

## Trace form

 $$335q - 2q^{2} - 2q^{3} + 336q^{4} + 2q^{5} + 2q^{6} - 6q^{8} + 331q^{9} + O(q^{10})$$ $$335q - 2q^{2} - 2q^{3} + 336q^{4} + 2q^{5} + 2q^{6} - 6q^{8} + 331q^{9} - 8q^{10} - 8q^{11} - 16q^{12} + 6q^{13} - 16q^{14} - 12q^{15} + 326q^{16} - 4q^{17} - 20q^{18} + 4q^{19} - 8q^{20} + 2q^{21} - 24q^{22} + 16q^{23} - 8q^{24} + 329q^{25} + 6q^{26} + 4q^{27} - 28q^{28} + 6q^{29} - 12q^{30} + 6q^{31} - 14q^{32} - 32q^{33} - 20q^{34} - 10q^{35} + 352q^{36} - 2q^{37} - 14q^{38} - 18q^{39} - 4q^{40} - 4q^{41} - 4q^{42} + 12q^{43} - 38q^{44} - 14q^{45} - 12q^{46} - 20q^{47} - 72q^{48} + 339q^{49} + 16q^{50} - 26q^{51} + 16q^{52} - 10q^{53} - 14q^{54} - 40q^{55} - 16q^{56} + 18q^{57} + 16q^{58} - 12q^{59} - 10q^{60} + 30q^{61} + 18q^{62} - 34q^{63} + 312q^{64} - 10q^{65} - 2q^{66} + 2q^{67} - 56q^{68} - 38q^{69} - 26q^{70} - 14q^{71} - 76q^{72} + 20q^{73} - 42q^{74} - 54q^{75} - 6q^{76} - 24q^{77} + 40q^{78} - 8q^{79} + 26q^{80} + 319q^{81} + 10q^{82} + 18q^{83} - 22q^{84} + 36q^{85} - 10q^{86} - 44q^{87} - 110q^{88} + 2q^{89} - 6q^{90} - 16q^{91} + 80q^{92} - 46q^{93} - 18q^{94} - 4q^{95} + 44q^{96} + 2q^{97} - 44q^{98} - 38q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(4019))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 4019
4019.2.a.a $$149$$ $$32.092$$ None $$-8$$ $$-12$$ $$-36$$ $$-32$$ $$+$$
4019.2.a.b $$186$$ $$32.092$$ None $$6$$ $$10$$ $$38$$ $$32$$ $$-$$