# Properties

 Label 684.3.p Level $684$ Weight $3$ Character orbit 684.p Rep. character $\chi_{684}(407,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $472$ Sturm bound $360$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$684 = 2^{2} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 684.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$684$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$360$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(684, [\chi])$$.

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

## Trace form

 $$472 q - 3 q^{2} + q^{4} - 9 q^{6} - 6 q^{9} + O(q^{10})$$ $$472 q - 3 q^{2} + q^{4} - 9 q^{6} - 6 q^{9} - 6 q^{10} - 27 q^{12} - 6 q^{13} - 6 q^{14} + q^{16} + 72 q^{17} + 12 q^{18} - 69 q^{20} - 6 q^{21} - 70 q^{24} - 2204 q^{25} - 18 q^{28} - 12 q^{29} + 25 q^{30} - 3 q^{32} - 66 q^{33} - 71 q^{36} - 3 q^{38} - 372 q^{41} + 7 q^{42} - 147 q^{44} + 42 q^{45} + 162 q^{48} + 1480 q^{49} + 75 q^{50} - 3 q^{52} - 339 q^{54} + 154 q^{57} - 10 q^{58} + 72 q^{60} - 4 q^{61} - 12 q^{62} - 272 q^{64} + 144 q^{65} - 389 q^{66} - 54 q^{68} + 54 q^{69} - 237 q^{72} - 16 q^{73} - 180 q^{74} - 189 q^{76} - 12 q^{77} - 30 q^{78} + 510 q^{80} + 298 q^{81} - 10 q^{82} + 288 q^{84} + 102 q^{85} + 159 q^{86} - 198 q^{90} + 897 q^{92} - 20 q^{93} - 24 q^{94} - 145 q^{96} + 174 q^{97} - 336 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(684, [\chi])$$ into newform subspaces

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