# Properties

 Label 2240.2.dh Level $2240$ Weight $2$ Character orbit 2240.dh Rep. character $\chi_{2240}(529,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $368$ Sturm bound $768$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.dh (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$560$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$768$$

## Dimensions

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

Total New Old
Modular forms 1600 400 1200
Cusp forms 1472 368 1104
Eisenstein series 128 32 96

## Trace form

 $$368q - 2q^{5} + O(q^{10})$$ $$368q - 2q^{5} + 4q^{11} + 16q^{15} + 4q^{19} + 4q^{21} - 16q^{29} + 56q^{31} - 18q^{35} - 16q^{45} - 16q^{49} + 28q^{51} - 12q^{59} - 4q^{61} - 4q^{65} + 8q^{69} - 10q^{75} + 8q^{79} + 112q^{81} - 28q^{85} + 80q^{91} - 20q^{95} + 112q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(2240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 3}$$