# Properties

 Label 2280.2.fn Level $2280$ Weight $2$ Character orbit 2280.fn Rep. character $\chi_{2280}(13,\cdot)$ Character field $\Q(\zeta_{36})$ Dimension $2880$ 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.fn (of order $$36$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$760$$ Character field: $$\Q(\zeta_{36})$$ Sturm bound: $$960$$

## Dimensions

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

Total New Old
Modular forms 5856 2880 2976
Cusp forms 5664 2880 2784
Eisenstein series 192 0 192

## Trace form

 $$2880q + 12q^{6} + O(q^{10})$$ $$2880q + 12q^{6} + 12q^{16} - 120q^{20} + 72q^{28} + 60q^{32} - 12q^{36} - 204q^{38} - 60q^{40} - 144q^{47} + 144q^{58} + 120q^{62} + 72q^{72} + 72q^{76} + 72q^{78} - 120q^{80} + 192q^{82} - 36q^{90} + 240q^{92} + O(q^{100})$$

## 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

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