# Properties

 Label 1323.2.ce Level $1323$ Weight $2$ Character orbit 1323.ce Rep. character $\chi_{1323}(20,\cdot)$ Character field $\Q(\zeta_{126})$ Dimension $5976$ Sturm bound $336$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.ce (of order $$126$$ and degree $$36$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1323$$ Character field: $$\Q(\zeta_{126})$$ Sturm bound: $$336$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1323, [\chi])$$.

Total New Old
Modular forms 6120 6120 0
Cusp forms 5976 5976 0
Eisenstein series 144 144 0

## Trace form

 $$5976q - 30q^{2} - 42q^{3} - 30q^{4} - 42q^{5} - 84q^{6} - 36q^{7} - 45q^{8} - 30q^{9} + O(q^{10})$$ $$5976q - 30q^{2} - 42q^{3} - 30q^{4} - 42q^{5} - 84q^{6} - 36q^{7} - 45q^{8} - 30q^{9} - 21q^{10} - 30q^{11} - 42q^{12} - 42q^{13} + 60q^{14} - 30q^{15} - 18q^{16} - 63q^{17} - 72q^{18} - 42q^{20} - 30q^{21} - 30q^{22} + 60q^{23} - 42q^{24} - 30q^{25} - 42q^{27} - 72q^{28} - 120q^{29} - 126q^{30} - 6q^{32} - 42q^{33} - 42q^{34} - 27q^{35} + 120q^{36} - 15q^{37} - 84q^{38} - 42q^{40} - 42q^{41} - 210q^{42} - 30q^{43} - 45q^{44} - 42q^{45} - 15q^{46} - 294q^{47} - 18q^{49} - 90q^{50} - 66q^{51} - 42q^{52} - 42q^{54} - 84q^{55} - 99q^{56} - 30q^{57} - 30q^{58} - 42q^{59} - 66q^{60} - 42q^{61} - 63q^{62} - 63q^{63} - 471q^{64} - 72q^{65} - 42q^{66} - 72q^{67} + 210q^{69} + 27q^{70} - 45q^{71} - 42q^{72} - 21q^{73} - 78q^{74} - 168q^{75} - 126q^{76} + 15q^{77} + 6q^{78} - 72q^{79} - 30q^{81} - 84q^{82} - 42q^{83} - 225q^{84} - 60q^{85} + 78q^{86} - 42q^{87} + 30q^{88} - 63q^{89} - 42q^{90} - 27q^{91} - 270q^{92} - 210q^{93} - 42q^{94} - 249q^{95} + 336q^{96} - 441q^{98} - 216q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1323, [\chi])$$ into newform subspaces

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