# Properties

 Label 2760.2.cl Level $2760$ Weight $2$ Character orbit 2760.cl Rep. character $\chi_{2760}(451,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $1920$ Sturm bound $1152$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2760.cl (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$184$$ Character field: $$\Q(\zeta_{22})$$ Sturm bound: $$1152$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2760, [\chi])$$.

Total New Old
Modular forms 5840 1920 3920
Cusp forms 5680 1920 3760
Eisenstein series 160 0 160

## Trace form

 $$1920q - 8q^{2} + 12q^{4} - 4q^{6} - 8q^{8} - 192q^{9} + O(q^{10})$$ $$1920q - 8q^{2} + 12q^{4} - 4q^{6} - 8q^{8} - 192q^{9} + 12q^{16} - 8q^{18} - 4q^{24} - 192q^{25} - 40q^{26} + 32q^{32} + 22q^{34} - 32q^{36} + 220q^{38} - 22q^{40} - 44q^{44} + 140q^{46} - 144q^{48} - 192q^{49} + 36q^{50} + 32q^{52} + 18q^{54} - 220q^{56} + 12q^{58} - 22q^{60} - 48q^{62} - 36q^{64} - 8q^{72} + 44q^{74} - 192q^{81} + 224q^{82} + 352q^{88} + 356q^{92} + 308q^{94} - 4q^{96} + 256q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2760, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2760, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2760, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(184, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(552, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(920, [\chi])$$$$^{\oplus 2}$$