Properties

 Label 2736.2.bb Level $2736$ Weight $2$ Character orbit 2736.bb Rep. character $\chi_{2736}(379,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $396$ Sturm bound $960$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2736.bb (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$304$$ Character field: $$\Q(i)$$ Sturm bound: $$960$$

Dimensions

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

Total New Old
Modular forms 976 404 572
Cusp forms 944 396 548
Eisenstein series 32 8 24

Trace form

 $$396q - 4q^{4} + 4q^{5} - 8q^{7} + O(q^{10})$$ $$396q - 4q^{4} + 4q^{5} - 8q^{7} + 4q^{11} - 12q^{16} + 8q^{17} - 10q^{19} + 32q^{20} + 8q^{23} - 32q^{26} + 48q^{35} - 36q^{38} - 4q^{43} + 20q^{44} + 364q^{49} - 8q^{55} + 24q^{58} - 36q^{61} - 44q^{62} + 32q^{64} + 40q^{68} + 40q^{74} + 12q^{76} + 32q^{77} - 40q^{80} - 12q^{82} + 44q^{83} + 8q^{85} + 32q^{92} + O(q^{100})$$

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

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

Decomposition of $$S_{2}^{\mathrm{old}}(2736, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2736, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(912, [\chi])$$$$^{\oplus 2}$$