# Properties

 Label 2280.2.dm Level $2280$ Weight $2$ Character orbit 2280.dm Rep. character $\chi_{2280}(163,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $960$ Sturm bound $960$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2280.dm (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$760$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$960$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2280, [\chi])$$.

Total New Old
Modular forms 1952 960 992
Cusp forms 1888 960 928
Eisenstein series 64 0 64

## Trace form

 $$960q + 4q^{6} + 24q^{8} + O(q^{10})$$ $$960q + 4q^{6} + 24q^{8} - 4q^{16} - 80q^{20} + 40q^{22} - 12q^{28} + 20q^{32} + 96q^{35} + 4q^{36} + 80q^{38} - 20q^{40} - 40q^{50} - 16q^{51} - 152q^{58} + 20q^{62} + 48q^{66} - 96q^{67} - 56q^{68} + 24q^{70} + 12q^{72} + 24q^{76} - 24q^{78} + 40q^{80} + 480q^{81} + 52q^{82} - 160q^{83} - 64q^{86} + 48q^{88} - 12q^{90} - 20q^{92} + 88q^{96} - 24q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2280, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2280, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(760, [\chi])$$$$^{\oplus 2}$$