# Properties

 Label 1805.2.x Level $1805$ Weight $2$ Character orbit 1805.x Rep. character $\chi_{1805}(18,\cdot)$ Character field $\Q(\zeta_{76})$ Dimension $6768$ Sturm bound $380$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1805 = 5 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1805.x (of order $$76$$ and degree $$36$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1805$$ Character field: $$\Q(\zeta_{76})$$ Sturm bound: $$380$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1805, [\chi])$$.

Total New Old
Modular forms 6912 6912 0
Cusp forms 6768 6768 0
Eisenstein series 144 144 0

## Trace form

 $$6768 q - 38 q^{2} - 38 q^{3} - 34 q^{5} - 60 q^{6} - 34 q^{7} - 38 q^{8} + O(q^{10})$$ $$6768 q - 38 q^{2} - 38 q^{3} - 34 q^{5} - 60 q^{6} - 34 q^{7} - 38 q^{8} - 38 q^{10} - 60 q^{11} - 38 q^{12} - 38 q^{13} - 38 q^{15} + 272 q^{16} - 46 q^{17} - 38 q^{18} - 70 q^{20} - 76 q^{21} - 228 q^{22} - 26 q^{23} - 18 q^{25} - 76 q^{26} - 38 q^{27} - 92 q^{28} + 2 q^{30} - 76 q^{31} - 38 q^{32} - 114 q^{33} - 22 q^{35} - 424 q^{36} - 38 q^{37} - 42 q^{38} - 38 q^{40} - 76 q^{41} - 38 q^{42} - 126 q^{43} - 268 q^{45} - 22 q^{47} - 38 q^{48} + 114 q^{50} - 228 q^{51} - 38 q^{52} - 38 q^{53} - 78 q^{55} + 152 q^{56} - 38 q^{57} + 50 q^{58} - 38 q^{60} - 52 q^{61} - 84 q^{62} - 106 q^{63} + 114 q^{65} - 52 q^{66} - 38 q^{67} - 156 q^{68} - 38 q^{70} - 76 q^{71} - 38 q^{72} - 54 q^{73} - 38 q^{75} - 56 q^{76} + 42 q^{77} - 38 q^{78} - 22 q^{80} + 260 q^{81} - 126 q^{82} + 22 q^{83} - 18 q^{85} + 608 q^{86} - 126 q^{87} - 38 q^{88} - 38 q^{90} - 152 q^{91} - 54 q^{92} + 58 q^{93} - 176 q^{95} + 720 q^{96} - 38 q^{97} - 38 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1805, [\chi])$$ into newform subspaces

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