# Properties

 Label 2736.2.dy Level $2736$ Weight $2$ Character orbit 2736.dy Rep. character $\chi_{2736}(83,\cdot)$ 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.dy (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

 $$1904q - 2q^{3} - 4q^{4} - 6q^{5} - 2q^{6} - 8q^{7} + O(q^{10})$$ $$1904q - 2q^{3} - 4q^{4} - 6q^{5} - 2q^{6} - 8q^{7} - 4q^{10} - 12q^{11} - 8q^{12} - 4q^{13} - 6q^{14} - 4q^{16} - 12q^{18} - 8q^{19} + 30q^{20} - 8q^{21} + 2q^{22} + 30q^{24} - 8q^{27} + 4q^{28} - 6q^{29} - 40q^{30} - 4q^{33} + 10q^{34} - 30q^{35} + 30q^{36} - 16q^{37} - 6q^{38} - 16q^{39} + 2q^{40} + 62q^{42} - 4q^{43} - 66q^{44} - 18q^{45} + 16q^{46} + 38q^{48} - 912q^{49} - 12q^{50} - 14q^{51} - 4q^{52} - 24q^{54} - 8q^{55} + 72q^{56} - 4q^{58} - 6q^{59} + 16q^{60} + 2q^{61} - 12q^{62} - 16q^{64} - 24q^{65} - 22q^{66} - 4q^{67} - 36q^{68} - 2q^{69} + 16q^{70} + 10q^{72} - 124q^{75} - 14q^{76} - 12q^{77} + 2q^{78} - 48q^{80} - 4q^{81} - 12q^{82} - 12q^{83} - 24q^{84} - 44q^{85} - 72q^{87} - 4q^{88} + 34q^{90} + 10q^{91} - 14q^{93} - 12q^{94} + 116q^{96} - 8q^{97} + 174q^{98} + 66q^{99} + O(q^{100})$$

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

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