# Properties

 Label 2015.2.hk Level 2015 Weight 2 Character orbit hk Rep. character $$\chi_{2015}(2,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 3520 Sturm bound 448

# Related objects

## Defining parameters

 Level: $$N$$ = $$2015 = 5 \cdot 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 2015.hk (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$2015$$ Character field: $$\Q(\zeta_{60})$$ Sturm bound: $$448$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2015, [\chi])$$.

Total New Old
Modular forms 3648 3648 0
Cusp forms 3520 3520 0
Eisenstein series 128 128 0

## Trace form

 $$3520q - 6q^{2} - 6q^{3} + 432q^{4} - 32q^{5} - 64q^{6} - 18q^{7} - 40q^{8} + O(q^{10})$$ $$3520q - 6q^{2} - 6q^{3} + 432q^{4} - 32q^{5} - 64q^{6} - 18q^{7} - 40q^{8} - 30q^{10} - 24q^{11} + 24q^{12} - 12q^{13} + 24q^{15} + 404q^{16} - 18q^{17} - 32q^{19} + 34q^{20} + 24q^{22} - 10q^{23} + 32q^{24} + 16q^{25} - 64q^{26} + 72q^{27} - 42q^{28} - 88q^{30} - 40q^{31} - 36q^{32} - 66q^{33} - 16q^{34} - 120q^{35} - 96q^{36} - 48q^{37} - 16q^{38} + 16q^{39} - 56q^{40} - 40q^{41} - 18q^{42} - 26q^{43} - 40q^{44} - 74q^{45} + 24q^{46} - 122q^{48} - 392q^{49} - 42q^{50} + 38q^{52} - 48q^{53} - 64q^{54} + 6q^{55} - 192q^{56} + 40q^{57} - 18q^{58} - 48q^{59} - 124q^{60} - 32q^{61} + 10q^{62} - 60q^{63} - 720q^{64} + 86q^{65} + 64q^{66} - 72q^{68} - 40q^{69} + 62q^{70} + 24q^{71} + 138q^{72} - 24q^{73} - 80q^{75} - 152q^{76} + 128q^{77} - 70q^{78} + 54q^{80} - 420q^{81} - 34q^{82} - 72q^{85} - 56q^{86} - 16q^{87} - 48q^{88} - 16q^{90} - 112q^{91} - 160q^{92} - 78q^{93} - 96q^{94} - 26q^{95} + 16q^{96} - 66q^{97} - 60q^{98} - 24q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2015, [\chi])$$ into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.