# Properties

 Label 2015.2.gw Level 2015 Weight 2 Character orbit gw Rep. character $$\chi_{2015}(127,\cdot)$$ 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.gw (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

 $$3520q - 18q^{2} - 4q^{3} - 96q^{6} - 30q^{7} + O(q^{10})$$ $$3520q - 18q^{2} - 4q^{3} - 96q^{6} - 30q^{7} - 6q^{10} - 36q^{11} - 18q^{12} - 14q^{13} - 30q^{15} - 420q^{16} - 10q^{17} - 42q^{18} + 96q^{21} - 50q^{22} - 22q^{23} - 16q^{25} - 48q^{26} + 20q^{27} - 36q^{28} - 120q^{30} + 30q^{32} - 162q^{33} + 12q^{35} + 3232q^{36} - 24q^{37} - 76q^{38} - 18q^{40} - 60q^{41} - 250q^{42} - 10q^{43} - 30q^{45} - 84q^{46} - 70q^{48} - 90q^{50} - 64q^{51} - 168q^{52} - 48q^{53} + 46q^{55} - 160q^{56} - 30q^{58} - 108q^{60} + 48q^{61} - 64q^{62} + 102q^{63} + 32q^{65} - 112q^{66} + 36q^{68} - 48q^{71} - 60q^{72} + 100q^{75} - 144q^{76} + 60q^{77} - 22q^{78} - 180q^{80} - 368q^{81} - 20q^{82} + 102q^{83} - 54q^{85} - 32q^{87} - 156q^{90} - 24q^{91} - 60q^{93} + 196q^{95} - 240q^{96} + 18q^{97} + 60q^{98} + O(q^{100})$$

## 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.