# Properties

 Label 2736.2.q Level $2736$ Weight $2$ Character orbit 2736.q Rep. character $\chi_{2736}(913,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $216$ Sturm bound $960$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2736.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Sturm bound: $$960$$

## Dimensions

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

Total New Old
Modular forms 984 216 768
Cusp forms 936 216 720
Eisenstein series 48 0 48

## Trace form

 $$216q + O(q^{10})$$ $$216q - 12q^{11} - 12q^{15} + 8q^{21} + 12q^{23} - 108q^{25} + 36q^{27} - 8q^{29} + 48q^{35} + 60q^{39} - 16q^{45} + 32q^{47} - 108q^{49} - 4q^{51} - 12q^{59} - 40q^{63} - 24q^{69} - 48q^{71} - 12q^{75} - 16q^{77} - 8q^{81} - 56q^{83} - 60q^{87} - 16q^{89} - 8q^{93} + 16q^{95} + 64q^{99} + O(q^{100})$$

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

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

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

$$S_{2}^{\mathrm{old}}(2736, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1368, [\chi])$$$$^{\oplus 2}$$