# Properties

 Label 4021.2.a Level 4021 Weight 2 Character orbit a Rep. character $$\chi_{4021}(1,\cdot)$$ Character field $$\Q$$ Dimension 334 Newform subspaces 3 Sturm bound 670 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$4021$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4021.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$670$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(4021))$$.

Total New Old
Modular forms 335 335 0
Cusp forms 334 334 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.

$$4021$$Dim.
$$+$$$$152$$
$$-$$$$182$$

## Trace form

 $$334q + 330q^{4} - 2q^{5} - 2q^{6} + 6q^{8} + 334q^{9} + O(q^{10})$$ $$334q + 330q^{4} - 2q^{5} - 2q^{6} + 6q^{8} + 334q^{9} - 6q^{10} + 10q^{11} + 2q^{12} - 12q^{13} + 6q^{14} - 6q^{15} + 326q^{16} - 8q^{17} - 8q^{18} - 6q^{19} - 2q^{20} - 24q^{21} + 16q^{22} + 2q^{23} + 2q^{24} + 336q^{25} + 8q^{26} + 6q^{27} - 4q^{28} - 4q^{29} + 2q^{31} + 22q^{32} + 6q^{33} - 8q^{34} + 14q^{35} + 354q^{36} - 4q^{37} - 12q^{38} - 8q^{39} - 50q^{40} + 8q^{41} + 28q^{42} - 2q^{43} + 46q^{44} - 4q^{45} - 28q^{46} - 2q^{47} - 10q^{48} + 328q^{49} + 6q^{50} + 8q^{51} - 42q^{52} - 8q^{53} + 14q^{54} - 6q^{55} + 32q^{56} - 22q^{57} - 28q^{58} + 40q^{59} - 64q^{60} - 42q^{61} - 16q^{62} - 38q^{63} + 314q^{64} - 34q^{65} - 6q^{66} - 10q^{67} - 26q^{68} - 32q^{69} - 14q^{70} - 8q^{71} - 2q^{72} - 22q^{74} - 42q^{75} - 60q^{76} - 6q^{77} - 52q^{78} + 16q^{79} - 36q^{80} + 310q^{81} - 36q^{82} + 18q^{83} - 136q^{84} + 6q^{85} - 34q^{86} - 24q^{87} - 10q^{88} - 38q^{89} - 130q^{90} - 16q^{91} - 36q^{94} + 10q^{95} - 14q^{96} + 6q^{97} - 8q^{98} + 100q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(4021))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 4021
4021.2.a.a $$1$$ $$32.108$$ $$\Q$$ None $$-2$$ $$1$$ $$3$$ $$4$$ $$+$$ $$q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots$$
4021.2.a.b $$151$$ $$32.108$$ None $$-16$$ $$-29$$ $$-27$$ $$-18$$ $$+$$
4021.2.a.c $$182$$ $$32.108$$ None $$18$$ $$28$$ $$22$$ $$14$$ $$-$$