# Properties

 Label 1805.2.w Level $1805$ Weight $2$ Character orbit 1805.w Rep. character $\chi_{1805}(11,\cdot)$ Character field $\Q(\zeta_{57})$ Dimension $4608$ Sturm bound $380$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1805 = 5 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1805.w (of order $$57$$ and degree $$36$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$361$$ Character field: $$\Q(\zeta_{57})$$ Sturm bound: $$380$$

## Dimensions

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

Total New Old
Modular forms 6912 4608 2304
Cusp forms 6768 4608 2160
Eisenstein series 144 0 144

## Trace form

 $$4608 q + 2 q^{2} - 36 q^{3} + 130 q^{4} - 4 q^{6} + 12 q^{7} - 12 q^{8} + 12 q^{9} + O(q^{10})$$ $$4608 q + 2 q^{2} - 36 q^{3} + 130 q^{4} - 4 q^{6} + 12 q^{7} - 12 q^{8} + 12 q^{9} + 8 q^{11} - 12 q^{12} - 6 q^{13} - 32 q^{14} + 4 q^{15} + 134 q^{16} + 120 q^{17} - 8 q^{18} + 2 q^{19} - 8 q^{21} + 146 q^{22} + 6 q^{23} - 6 q^{24} + 128 q^{25} - 170 q^{26} + 60 q^{27} - 6 q^{29} + 16 q^{31} + 24 q^{32} + 24 q^{33} - 10 q^{34} - 2 q^{35} + 106 q^{36} - 8 q^{37} + 82 q^{38} + 12 q^{39} + 18 q^{40} - 16 q^{41} - 50 q^{42} - 308 q^{43} - 44 q^{44} + 8 q^{45} - 14 q^{46} - 126 q^{47} + 852 q^{48} - 376 q^{49} - 4 q^{50} - 72 q^{51} - 42 q^{52} + 374 q^{54} - 442 q^{56} + 28 q^{57} + 84 q^{58} - 14 q^{59} - 32 q^{60} - 12 q^{61} + 12 q^{62} - 200 q^{63} - 296 q^{64} - 40 q^{65} - 18 q^{66} - 14 q^{67} - 52 q^{68} - 124 q^{69} - 8 q^{70} - 12 q^{71} + 28 q^{72} - 42 q^{73} - 82 q^{74} - 4 q^{75} - 198 q^{76} + 28 q^{77} - 520 q^{78} - 2 q^{79} - 160 q^{80} - 174 q^{81} - 120 q^{82} - 42 q^{83} + 128 q^{84} - 8 q^{85} + 584 q^{86} - 154 q^{87} + 32 q^{88} - 132 q^{89} + 660 q^{90} + 64 q^{91} + 28 q^{92} - 4 q^{93} - 284 q^{94} + 12 q^{95} - 66 q^{96} - 98 q^{97} - 158 q^{98} + 12 q^{99} + O(q^{100})$$

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

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1805, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1805, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(361, [\chi])$$$$^{\oplus 2}$$