# Properties

 Label 2736.2.ef Level $2736$ Weight $2$ Character orbit 2736.ef Rep. character $\chi_{2736}(349,\cdot)$ 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.ef (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

 $$1904q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 2q^{6} - 16q^{8} + O(q^{10})$$ $$1904q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 2q^{6} - 16q^{8} - 4q^{10} - 4q^{11} - 8q^{12} - 4q^{13} + 10q^{14} - 4q^{15} - 4q^{16} - 8q^{17} - 4q^{18} - 8q^{19} - 18q^{20} + 4q^{21} + 2q^{22} + 30q^{24} - 48q^{26} - 8q^{27} - 12q^{28} + 2q^{29} - 40q^{30} - 8q^{31} - 4q^{32} - 4q^{33} - 6q^{34} - 14q^{35} + 30q^{36} - 16q^{37} - 58q^{38} + 2q^{40} + 14q^{42} - 4q^{43} + 18q^{44} + 2q^{45} - 32q^{46} + 4q^{47} - 42q^{48} + 896q^{49} + 4q^{50} + 10q^{51} - 4q^{52} - 4q^{53} - 24q^{54} - 16q^{56} - 4q^{58} + 2q^{59} - 48q^{60} + 2q^{61} - 88q^{62} - 60q^{63} - 16q^{64} - 8q^{65} + 18q^{66} - 4q^{67} + 4q^{68} - 2q^{69} - 12q^{70} + 42q^{72} + 52q^{74} + 100q^{75} + 10q^{76} - 60q^{77} + 2q^{78} - 8q^{79} - 20q^{80} - 4q^{81} + 4q^{82} - 4q^{83} - 80q^{84} + 36q^{85} - 4q^{86} - 4q^{88} + 34q^{90} - 18q^{91} + 60q^{92} + 10q^{93} - 12q^{94} - 4q^{95} + 4q^{96} - 8q^{97} - 82q^{98} - 6q^{99} + O(q^{100})$$

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

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