# Properties

 Label 2240.2.dy Level $2240$ Weight $2$ Character orbit 2240.dy Rep. character $\chi_{2240}(251,\cdot)$ Character field $\Q(\zeta_{16})$ Dimension $2048$ Sturm bound $768$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.dy (of order $$16$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$448$$ Character field: $$\Q(\zeta_{16})$$ Sturm bound: $$768$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2240, [\chi])$$.

Total New Old
Modular forms 3104 2048 1056
Cusp forms 3040 2048 992
Eisenstein series 64 0 64

## Trace form

 $$2048q + O(q^{10})$$ $$2048q + 16q^{22} - 80q^{28} - 80q^{42} + 16q^{44} - 192q^{64} - 160q^{67} + 128q^{71} + 16q^{74} - 192q^{78} + 112q^{84} + 272q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2240, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2240, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(448, [\chi])$$$$^{\oplus 2}$$