# Properties

 Label 2736.3.bs Level $2736$ Weight $3$ Character orbit 2736.bs Rep. character $\chi_{2736}(1633,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $476$ Sturm bound $1440$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2736.bs (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$171$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$1440$$

## Dimensions

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

Total New Old
Modular forms 1944 484 1460
Cusp forms 1896 476 1420
Eisenstein series 48 8 40

## Trace form

 $$476q - 2q^{5} + 2q^{7} + 4q^{9} + O(q^{10})$$ $$476q - 2q^{5} + 2q^{7} + 4q^{9} + 2q^{11} + 40q^{17} + 4q^{19} + 2q^{23} - 1152q^{25} - 92q^{35} + 22q^{39} + 98q^{43} + 46q^{45} + 2q^{47} - 1584q^{49} - 92q^{55} - 44q^{57} - 2q^{61} - 238q^{63} + 40q^{73} + 194q^{77} + 260q^{81} + 2q^{83} - 52q^{85} + 246q^{87} - 22q^{93} + 242q^{95} - 94q^{99} + O(q^{100})$$

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

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

## Decomposition of $$S_{3}^{\mathrm{old}}(2736, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(2736, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(1368, [\chi])$$$$^{\oplus 2}$$