# Properties

 Label 1840.2.cf Level $1840$ Weight $2$ Character orbit 1840.cf Rep. character $\chi_{1840}(53,\cdot)$ 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.cf (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

 $$5680q - 18q^{2} - 36q^{3} - 8q^{4} - 22q^{5} - 36q^{6} - 18q^{8} - 552q^{9} + O(q^{10})$$ $$5680q - 18q^{2} - 36q^{3} - 8q^{4} - 22q^{5} - 36q^{6} - 18q^{8} - 552q^{9} - 22q^{10} - 44q^{11} - 6q^{12} - 36q^{13} - 44q^{15} - 28q^{16} - 44q^{17} + 2q^{18} - 22q^{20} - 44q^{21} + 24q^{24} - 36q^{26} - 12q^{27} - 22q^{28} - 22q^{30} - 72q^{31} + 2q^{32} - 44q^{33} - 38q^{35} - 36q^{36} - 44q^{37} - 22q^{38} + 48q^{39} - 22q^{40} - 242q^{42} - 264q^{44} - 24q^{46} - 80q^{47} + 78q^{48} + 2q^{50} - 44q^{51} + 142q^{52} + 40q^{54} - 44q^{56} - 58q^{58} - 22q^{60} - 44q^{61} - 26q^{62} - 44q^{63} - 32q^{64} - 44q^{65} - 44q^{66} - 4q^{69} + 20q^{70} - 40q^{72} - 6q^{75} - 44q^{76} - 26q^{78} - 22q^{80} - 576q^{81} - 26q^{82} - 44q^{83} - 38q^{85} - 44q^{86} + 24q^{87} - 22q^{88} - 66q^{90} + 34q^{92} - 56q^{93} - 8q^{94} - 36q^{95} - 36q^{96} - 44q^{97} - 26q^{98} + O(q^{100})$$

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

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