# Properties

 Label 2736.2.dt Level $2736$ Weight $2$ Character orbit 2736.dt Rep. character $\chi_{2736}(331,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $1904$ Sturm bound $960$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2736.dt (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2736$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$960$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2736, [\chi])$$.

Total New Old
Modular forms 1936 1936 0
Cusp forms 1904 1904 0
Eisenstein series 32 32 0

## Trace form

 $$1904q - 6q^{2} - 6q^{3} + 2q^{4} - 4q^{5} - 2q^{6} - 8q^{7} + O(q^{10})$$ $$1904q - 6q^{2} - 6q^{3} + 2q^{4} - 4q^{5} - 2q^{6} - 8q^{7} - 12q^{10} - 4q^{11} - 6q^{13} + 2q^{16} - 8q^{17} + 12q^{18} - 8q^{19} + 10q^{20} - 6q^{21} + 4q^{23} + 14q^{24} - 48q^{26} + 4q^{28} + 16q^{30} - 6q^{32} - 12q^{33} + 6q^{35} - 18q^{36} - 30q^{38} - 16q^{39} + 6q^{42} + 2q^{43} + 18q^{44} + 2q^{45} - 6q^{48} - 912q^{49} + 24q^{50} - 6q^{51} - 6q^{52} - 12q^{53} - 46q^{54} - 8q^{55} + 120q^{56} - 4q^{58} - 6q^{60} - 4q^{61} - 88q^{62} - 16q^{64} - 66q^{66} - 6q^{67} + 4q^{68} + 18q^{69} - 24q^{71} + 30q^{72} + 30q^{74} + 48q^{75} + 22q^{76} + 52q^{77} - 6q^{78} + 12q^{80} - 4q^{81} - 12q^{82} - 4q^{83} - 18q^{85} - 6q^{86} - 72q^{87} + 102q^{90} + 30q^{91} + 34q^{92} - 8q^{93} + 24q^{94} - 20q^{96} - 12q^{97} + 42q^{98} + 80q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2736, [\chi])$$ into newform subspaces

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