# Properties

 Label 618.2 Level 618 Weight 2 Dimension 2653 Nonzero newspaces 8 Newform subspaces 31 Sturm bound 42432 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$618 = 2 \cdot 3 \cdot 103$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$31$$ Sturm bound: $$42432$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(618))$$.

Total New Old
Modular forms 11016 2653 8363
Cusp forms 10201 2653 7548
Eisenstein series 815 0 815

## Trace form

 $$2653q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$2653q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + 6q^{10} + 12q^{11} + q^{12} + 14q^{13} + 8q^{14} + 6q^{15} + q^{16} + 18q^{17} + q^{18} + 20q^{19} + 6q^{20} + 8q^{21} + 12q^{22} + 24q^{23} + q^{24} + 31q^{25} + 14q^{26} + q^{27} + 8q^{28} + 30q^{29} + 6q^{30} + 32q^{31} + q^{32} + 12q^{33} + 18q^{34} + 48q^{35} + q^{36} + 38q^{37} + 20q^{38} + 14q^{39} + 6q^{40} + 42q^{41} + 8q^{42} + 44q^{43} + 12q^{44} + 6q^{45} + 24q^{46} + 48q^{47} + q^{48} + 57q^{49} + 31q^{50} + 18q^{51} + 14q^{52} + 54q^{53} + q^{54} + 72q^{55} + 8q^{56} + 20q^{57} + 30q^{58} + 60q^{59} + 6q^{60} + 62q^{61} + 32q^{62} + 8q^{63} + q^{64} + 84q^{65} + 12q^{66} + 68q^{67} + 18q^{68} + 24q^{69} + 48q^{70} + 72q^{71} + q^{72} + 74q^{73} + 38q^{74} + 31q^{75} + 20q^{76} + 96q^{77} + 14q^{78} + 80q^{79} + 6q^{80} + q^{81} + 42q^{82} + 84q^{83} - 26q^{84} - 300q^{85} - 160q^{86} - 174q^{87} + 12q^{88} - 318q^{89} - 96q^{90} - 772q^{91} - 180q^{92} - 376q^{93} - 360q^{94} - 492q^{95} + q^{96} - 786q^{97} - 759q^{98} - 192q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(618))$$

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
618.2.a $$\chi_{618}(1, \cdot)$$ 618.2.a.a 1 1
618.2.a.b 1
618.2.a.c 1
618.2.a.d 1
618.2.a.e 1
618.2.a.f 1
618.2.a.g 1
618.2.a.h 2
618.2.a.i 2
618.2.a.j 2
618.2.a.k 4
618.2.d $$\chi_{618}(617, \cdot)$$ 618.2.d.a 36 1
618.2.e $$\chi_{618}(355, \cdot)$$ 618.2.e.a 2 2
618.2.e.b 2
618.2.e.c 6
618.2.e.d 8
618.2.e.e 8
618.2.e.f 10
618.2.f $$\chi_{618}(47, \cdot)$$ 618.2.f.a 4 2
618.2.f.b 64
618.2.i $$\chi_{618}(13, \cdot)$$ 618.2.i.a 16 16
618.2.i.b 32
618.2.i.c 64
618.2.i.d 64
618.2.i.e 80
618.2.j $$\chi_{618}(89, \cdot)$$ 618.2.j.a 576 16
618.2.m $$\chi_{618}(7, \cdot)$$ 618.2.m.a 128 32
618.2.m.b 128
618.2.m.c 160
618.2.m.d 160
618.2.p $$\chi_{618}(5, \cdot)$$ 618.2.p.a 1088 32

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(618))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(618)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(103))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(206))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(309))$$$$^{\oplus 2}$$