# Properties

 Label 619.2 Level 619 Weight 2 Dimension 15657 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 63860 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$619$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$63860$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(619))$$.

Total New Old
Modular forms 16274 16274 0
Cusp forms 15657 15657 0
Eisenstein series 617 617 0

## Trace form

 $$15657q - 306q^{2} - 305q^{3} - 302q^{4} - 303q^{5} - 297q^{6} - 301q^{7} - 294q^{8} - 296q^{9} + O(q^{10})$$ $$15657q - 306q^{2} - 305q^{3} - 302q^{4} - 303q^{5} - 297q^{6} - 301q^{7} - 294q^{8} - 296q^{9} - 291q^{10} - 297q^{11} - 281q^{12} - 295q^{13} - 285q^{14} - 285q^{15} - 278q^{16} - 291q^{17} - 270q^{18} - 289q^{19} - 267q^{20} - 277q^{21} - 273q^{22} - 285q^{23} - 249q^{24} - 278q^{25} - 267q^{26} - 269q^{27} - 253q^{28} - 279q^{29} - 237q^{30} - 277q^{31} - 246q^{32} - 261q^{33} - 255q^{34} - 261q^{35} - 218q^{36} - 271q^{37} - 249q^{38} - 253q^{39} - 219q^{40} - 267q^{41} - 213q^{42} - 265q^{43} - 225q^{44} - 231q^{45} - 237q^{46} - 261q^{47} - 185q^{48} - 252q^{49} - 216q^{50} - 237q^{51} - 211q^{52} - 255q^{53} - 189q^{54} - 237q^{55} - 189q^{56} - 229q^{57} - 219q^{58} - 249q^{59} - 141q^{60} - 247q^{61} - 213q^{62} - 205q^{63} - 182q^{64} - 225q^{65} - 165q^{66} - 241q^{67} - 183q^{68} - 213q^{69} - 165q^{70} - 237q^{71} - 114q^{72} - 235q^{73} - 195q^{74} - 185q^{75} - 169q^{76} - 213q^{77} - 141q^{78} - 229q^{79} - 123q^{80} - 188q^{81} - 183q^{82} - 225q^{83} - 85q^{84} - 201q^{85} - 177q^{86} - 189q^{87} - 129q^{88} - 219q^{89} - 75q^{90} - 197q^{91} - 141q^{92} - 181q^{93} - 165q^{94} - 189q^{95} - 57q^{96} - 211q^{97} - 138q^{98} - 153q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(619))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
619.2.a $$\chi_{619}(1, \cdot)$$ 619.2.a.a 21 1
619.2.a.b 30
619.2.c $$\chi_{619}(252, \cdot)$$ 619.2.c.a 102 2
619.2.e $$\chi_{619}(9, \cdot)$$ 619.2.e.a 5100 102
619.2.g $$\chi_{619}(4, \cdot)$$ 619.2.g.a 10404 204

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database