# Properties

 Label 2736.3.ej Level $2736$ Weight $3$ Character orbit 2736.ej Rep. character $\chi_{2736}(653,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $3824$ Sturm bound $1440$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2736.ej (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2736$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$1440$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(2736, [\chi])$$.

Total New Old
Modular forms 3856 3856 0
Cusp forms 3824 3824 0
Eisenstein series 32 32 0

## Trace form

 $$3824q - 6q^{2} - 2q^{3} + 2q^{4} - 2q^{6} + O(q^{10})$$ $$3824q - 6q^{2} - 2q^{3} + 2q^{4} - 2q^{6} - 4q^{10} - 12q^{11} - 8q^{12} + 2q^{13} - 4q^{15} + 2q^{16} - 16q^{18} - 8q^{19} - 138q^{20} - 38q^{21} - 4q^{22} - 18q^{24} - 8q^{27} - 36q^{28} - 196q^{30} - 8q^{31} - 6q^{32} - 4q^{33} - 36q^{34} - 150q^{35} - 66q^{36} - 16q^{37} - 6q^{38} - 4q^{40} + 170q^{42} + 2q^{43} - 198q^{44} - 58q^{45} + 136q^{46} + 558q^{48} + 13040q^{49} - 12q^{50} - 38q^{51} + 2q^{52} + 306q^{54} - 600q^{56} - 4q^{58} + 426q^{60} - 4q^{61} - 24q^{62} + 192q^{63} - 16q^{64} - 24q^{65} + 630q^{66} + 2q^{67} - 108q^{68} - 26q^{69} + 192q^{70} - 102q^{72} + 246q^{74} + 508q^{75} + 310q^{76} - 12q^{77} + 14q^{78} + 4q^{79} - 720q^{80} - 4q^{81} - 20q^{82} - 12q^{83} - 776q^{84} + 102q^{85} - 6q^{86} - 4q^{88} - 146q^{90} - 102q^{91} - 6q^{92} - 20q^{93} + 12q^{94} - 12q^{95} - 716q^{96} + 4q^{97} - 930q^{98} - 420q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(2736, [\chi])$$ into newform subspaces

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