# Properties

 Label 619.2.a Level 619 Weight 2 Character orbit a Rep. character $$\chi_{619}(1,\cdot)$$ Character field $$\Q$$ Dimension 51 Newform subspaces 2 Sturm bound 103 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$619$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 619.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$103$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(619))$$.

Total New Old
Modular forms 52 52 0
Cusp forms 51 51 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.

$$619$$Dim.
$$+$$$$21$$
$$-$$$$30$$

## Trace form

 $$51q - 4q^{3} + 48q^{4} - 2q^{7} + 6q^{8} + 49q^{9} + O(q^{10})$$ $$51q - 4q^{3} + 48q^{4} - 2q^{7} + 6q^{8} + 49q^{9} + 6q^{10} - 4q^{11} - 14q^{12} - 2q^{13} - 12q^{14} - 12q^{15} + 46q^{16} - 10q^{17} - 4q^{18} - 16q^{19} + 4q^{20} - 12q^{21} + 12q^{22} - 10q^{23} - 4q^{24} + 51q^{25} - 10q^{26} - 10q^{27} - 12q^{28} + 12q^{29} - 30q^{30} - 6q^{31} + 2q^{32} - 12q^{33} - 2q^{34} + 6q^{35} + 32q^{36} - 4q^{37} + 26q^{38} + 28q^{39} + 14q^{42} - 2q^{43} + 2q^{44} - 6q^{45} - 16q^{46} - 8q^{47} - 34q^{48} + 47q^{49} + 8q^{50} - 8q^{51} + 6q^{52} - 2q^{53} - 32q^{54} + 6q^{55} - 26q^{56} - 32q^{57} + 52q^{58} - 4q^{59} - 56q^{60} - 6q^{61} + 70q^{62} - 46q^{63} + 86q^{64} - 22q^{65} - 30q^{66} + 4q^{67} - 68q^{68} - 24q^{69} + 4q^{70} - 14q^{71} + 18q^{72} - 6q^{73} + 4q^{74} - 50q^{75} - 46q^{76} - 18q^{77} - 20q^{78} + 8q^{79} + 36q^{80} + 11q^{81} + 4q^{82} - 12q^{83} - 56q^{84} - 10q^{85} - 34q^{86} + 24q^{87} + 14q^{88} + 46q^{89} + 58q^{90} - 34q^{91} + 28q^{92} - 30q^{93} - 12q^{94} + 6q^{95} - 56q^{96} + 12q^{97} + 24q^{98} - 46q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(619))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 619
619.2.a.a $$21$$ $$4.943$$ None $$-9$$ $$-5$$ $$-21$$ $$-4$$ $$+$$
619.2.a.b $$30$$ $$4.943$$ None $$9$$ $$1$$ $$21$$ $$2$$ $$-$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database