Properties

 Label 6029.2.a Level 6029 Weight 2 Character orbit a Rep. character $$\chi_{6029}(1,\cdot)$$ Character field $$\Q$$ Dimension 502 Newforms 2 Sturm bound 1005 Trace bound 1

Related objects

Defining parameters

 Level: $$N$$ = $$6029$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6029.a (trivial) Character field: $$\Q$$ Newforms: $$2$$ Sturm bound: $$1005$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(6029))$$.

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.

$$6029$$Dim.
$$+$$$$234$$
$$-$$$$268$$

Trace form

 $$502q$$ $$\mathstrut -\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 502q^{4}$$ $$\mathstrut -\mathstrut 6q^{5}$$ $$\mathstrut -\mathstrut 6q^{6}$$ $$\mathstrut -\mathstrut 2q^{7}$$ $$\mathstrut -\mathstrut 6q^{8}$$ $$\mathstrut +\mathstrut 498q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$502q$$ $$\mathstrut -\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 502q^{4}$$ $$\mathstrut -\mathstrut 6q^{5}$$ $$\mathstrut -\mathstrut 6q^{6}$$ $$\mathstrut -\mathstrut 2q^{7}$$ $$\mathstrut -\mathstrut 6q^{8}$$ $$\mathstrut +\mathstrut 498q^{9}$$ $$\mathstrut +\mathstrut 2q^{10}$$ $$\mathstrut -\mathstrut 6q^{11}$$ $$\mathstrut +\mathstrut 2q^{12}$$ $$\mathstrut -\mathstrut 4q^{13}$$ $$\mathstrut -\mathstrut 6q^{15}$$ $$\mathstrut +\mathstrut 498q^{16}$$ $$\mathstrut +\mathstrut 6q^{18}$$ $$\mathstrut +\mathstrut 10q^{19}$$ $$\mathstrut -\mathstrut 22q^{20}$$ $$\mathstrut +\mathstrut 4q^{21}$$ $$\mathstrut -\mathstrut 12q^{22}$$ $$\mathstrut -\mathstrut 4q^{23}$$ $$\mathstrut -\mathstrut 18q^{24}$$ $$\mathstrut +\mathstrut 484q^{25}$$ $$\mathstrut -\mathstrut 20q^{26}$$ $$\mathstrut -\mathstrut 30q^{28}$$ $$\mathstrut -\mathstrut 22q^{29}$$ $$\mathstrut +\mathstrut 10q^{30}$$ $$\mathstrut +\mathstrut 6q^{31}$$ $$\mathstrut -\mathstrut 14q^{32}$$ $$\mathstrut +\mathstrut 6q^{33}$$ $$\mathstrut -\mathstrut 20q^{34}$$ $$\mathstrut -\mathstrut 14q^{35}$$ $$\mathstrut +\mathstrut 472q^{36}$$ $$\mathstrut +\mathstrut 2q^{38}$$ $$\mathstrut -\mathstrut 8q^{39}$$ $$\mathstrut +\mathstrut 10q^{40}$$ $$\mathstrut +\mathstrut 2q^{41}$$ $$\mathstrut +\mathstrut 16q^{42}$$ $$\mathstrut -\mathstrut 2q^{43}$$ $$\mathstrut -\mathstrut 30q^{44}$$ $$\mathstrut -\mathstrut 42q^{45}$$ $$\mathstrut -\mathstrut 12q^{46}$$ $$\mathstrut +\mathstrut 14q^{47}$$ $$\mathstrut -\mathstrut 24q^{48}$$ $$\mathstrut +\mathstrut 504q^{49}$$ $$\mathstrut -\mathstrut 12q^{50}$$ $$\mathstrut +\mathstrut 28q^{51}$$ $$\mathstrut -\mathstrut 24q^{52}$$ $$\mathstrut -\mathstrut 30q^{53}$$ $$\mathstrut -\mathstrut 28q^{54}$$ $$\mathstrut -\mathstrut 40q^{55}$$ $$\mathstrut -\mathstrut 46q^{56}$$ $$\mathstrut +\mathstrut 30q^{57}$$ $$\mathstrut -\mathstrut 32q^{58}$$ $$\mathstrut -\mathstrut 2q^{59}$$ $$\mathstrut -\mathstrut 30q^{60}$$ $$\mathstrut +\mathstrut 4q^{61}$$ $$\mathstrut -\mathstrut 20q^{62}$$ $$\mathstrut +\mathstrut 6q^{63}$$ $$\mathstrut +\mathstrut 476q^{64}$$ $$\mathstrut -\mathstrut 2q^{65}$$ $$\mathstrut -\mathstrut 104q^{66}$$ $$\mathstrut -\mathstrut 18q^{67}$$ $$\mathstrut -\mathstrut 44q^{68}$$ $$\mathstrut -\mathstrut 14q^{69}$$ $$\mathstrut -\mathstrut 12q^{70}$$ $$\mathstrut -\mathstrut 4q^{71}$$ $$\mathstrut -\mathstrut 12q^{72}$$ $$\mathstrut +\mathstrut 6q^{73}$$ $$\mathstrut -\mathstrut 52q^{74}$$ $$\mathstrut -\mathstrut 6q^{75}$$ $$\mathstrut +\mathstrut 36q^{76}$$ $$\mathstrut -\mathstrut 24q^{77}$$ $$\mathstrut -\mathstrut 88q^{78}$$ $$\mathstrut -\mathstrut 26q^{79}$$ $$\mathstrut -\mathstrut 72q^{80}$$ $$\mathstrut +\mathstrut 478q^{81}$$ $$\mathstrut +\mathstrut 38q^{82}$$ $$\mathstrut -\mathstrut 26q^{83}$$ $$\mathstrut -\mathstrut 12q^{84}$$ $$\mathstrut -\mathstrut 32q^{85}$$ $$\mathstrut +\mathstrut 28q^{86}$$ $$\mathstrut +\mathstrut 2q^{87}$$ $$\mathstrut -\mathstrut 16q^{88}$$ $$\mathstrut -\mathstrut 14q^{89}$$ $$\mathstrut -\mathstrut 2q^{90}$$ $$\mathstrut -\mathstrut 12q^{91}$$ $$\mathstrut -\mathstrut 6q^{92}$$ $$\mathstrut +\mathstrut 6q^{93}$$ $$\mathstrut +\mathstrut 32q^{94}$$ $$\mathstrut -\mathstrut 16q^{95}$$ $$\mathstrut -\mathstrut 28q^{96}$$ $$\mathstrut -\mathstrut 18q^{97}$$ $$\mathstrut -\mathstrut 32q^{98}$$ $$\mathstrut -\mathstrut 64q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(6029))$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 6029
6029.2.a.a $$234$$ $$48.142$$ None $$-10$$ $$-43$$ $$-24$$ $$-61$$ $$+$$
6029.2.a.b $$268$$ $$48.142$$ None $$8$$ $$43$$ $$18$$ $$59$$ $$-$$