# Properties

 Label 2736.2.ha Level $2736$ Weight $2$ Character orbit 2736.ha Rep. character $\chi_{2736}(253,\cdot)$ Character field $\Q(\zeta_{36})$ Dimension $2376$ Sturm bound $960$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2736.ha (of order $$36$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$304$$ Character field: $$\Q(\zeta_{36})$$ Sturm bound: $$960$$

## Dimensions

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

Total New Old
Modular forms 5856 2424 3432
Cusp forms 5664 2376 3288
Eisenstein series 192 48 144

## Trace form

 $$2376q + 12q^{2} - 12q^{4} + 12q^{5} + 6q^{8} + O(q^{10})$$ $$2376q + 12q^{2} - 12q^{4} + 12q^{5} + 6q^{8} - 42q^{10} + 6q^{11} - 12q^{13} + 24q^{14} + 24q^{17} - 12q^{19} + 24q^{20} - 12q^{22} + 54q^{26} - 36q^{28} + 12q^{29} + 60q^{31} - 18q^{32} - 72q^{34} + 42q^{35} - 24q^{37} + 126q^{38} + 18q^{40} - 12q^{43} - 54q^{44} + 24q^{46} + 24q^{47} + 1104q^{49} - 12q^{50} - 60q^{52} + 12q^{53} + 108q^{56} - 24q^{58} + 12q^{59} - 12q^{61} - 6q^{64} + 12q^{65} - 12q^{67} + 42q^{68} - 126q^{70} + 96q^{74} + 36q^{76} + 108q^{77} - 24q^{79} + 72q^{80} + 48q^{82} + 6q^{83} - 108q^{85} + 12q^{86} - 6q^{88} - 54q^{91} + 12q^{92} + 60q^{94} + 24q^{95} - 24q^{97} + 84q^{98} + O(q^{100})$$

## 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

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