# Properties

 Label 1045.2.cs Level $1045$ Weight $2$ Character orbit 1045.cs Rep. character $\chi_{1045}(17,\cdot)$ Character field $\Q(\zeta_{180})$ Dimension $5568$ Sturm bound $240$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1045.cs (of order $$180$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1045$$ Character field: $$\Q(\zeta_{180})$$ Sturm bound: $$240$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1045, [\chi])$$.

Total New Old
Modular forms 5952 5952 0
Cusp forms 5568 5568 0
Eisenstein series 384 384 0

## Trace form

 $$5568 q - 60 q^{2} - 36 q^{3} - 36 q^{5} - 120 q^{6} - 60 q^{7} - 30 q^{8} + O(q^{10})$$ $$5568 q - 60 q^{2} - 36 q^{3} - 36 q^{5} - 120 q^{6} - 60 q^{7} - 30 q^{8} - 48 q^{11} - 48 q^{12} - 60 q^{13} - 36 q^{15} - 72 q^{16} - 60 q^{17} - 120 q^{18} - 252 q^{20} - 60 q^{22} - 96 q^{23} - 108 q^{25} - 156 q^{26} - 18 q^{27} - 60 q^{28} - 30 q^{30} - 36 q^{31} - 6 q^{33} - 60 q^{35} - 72 q^{36} - 72 q^{37} - 204 q^{38} - 60 q^{40} - 300 q^{41} + 36 q^{42} - 48 q^{45} - 60 q^{46} + 12 q^{47} - 36 q^{48} - 30 q^{50} - 120 q^{51} - 60 q^{52} + 18 q^{53} - 222 q^{55} - 384 q^{56} - 300 q^{57} - 216 q^{58} + 108 q^{60} - 120 q^{61} + 60 q^{62} - 60 q^{63} - 48 q^{66} - 336 q^{67} + 90 q^{68} + 60 q^{70} - 72 q^{71} + 120 q^{72} - 60 q^{73} - 72 q^{75} + 120 q^{77} - 372 q^{78} - 72 q^{80} + 24 q^{81} - 72 q^{82} - 30 q^{83} + 180 q^{85} - 72 q^{86} + 132 q^{88} - 300 q^{90} - 156 q^{91} - 132 q^{92} - 156 q^{93} - 60 q^{95} + 720 q^{96} + 12 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1045, [\chi])$$ into newform subspaces

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