# Properties

 Label 1840.2.cj Level $1840$ Weight $2$ Character orbit 1840.cj Rep. character $\chi_{1840}(19,\cdot)$ Character field $\Q(\zeta_{44})$ Dimension $5680$ Sturm bound $576$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.cj (of order $$44$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1840$$ Character field: $$\Q(\zeta_{44})$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1840, [\chi])$$.

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

## Trace form

 $$5680q - 36q^{4} - 22q^{5} - 36q^{6} + O(q^{10})$$ $$5680q - 36q^{4} - 22q^{5} - 36q^{6} - 22q^{10} - 44q^{11} - 44q^{14} - 44q^{16} - 44q^{19} - 22q^{20} - 44q^{21} - 72q^{24} - 76q^{26} - 36q^{29} - 22q^{30} + 2q^{35} - 100q^{36} - 72q^{39} - 22q^{40} - 44q^{44} - 32q^{46} - 592q^{49} + 62q^{50} - 44q^{51} - 228q^{54} - 36q^{55} - 44q^{56} - 36q^{59} - 22q^{60} - 44q^{61} + 12q^{64} - 44q^{65} - 44q^{66} - 68q^{69} + 24q^{70} - 72q^{71} - 44q^{74} - 6q^{75} - 44q^{76} - 22q^{80} + 432q^{81} - 44q^{84} + 2q^{85} - 44q^{86} - 22q^{90} - 164q^{94} - 116q^{96} - 44q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1840, [\chi])$$ into newform subspaces

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