Properties

 Label 1323.2.ci Level $1323$ Weight $2$ Character orbit 1323.ci Rep. character $\chi_{1323}(5,\cdot)$ 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.ci (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

 $$5976q - 39q^{2} - 33q^{3} - 39q^{4} - 33q^{5} - 66q^{6} - 36q^{7} - 45q^{8} - 39q^{9} + O(q^{10})$$ $$5976q - 39q^{2} - 33q^{3} - 39q^{4} - 33q^{5} - 66q^{6} - 36q^{7} - 45q^{8} - 39q^{9} - 21q^{10} - 39q^{11} - 33q^{12} - 42q^{13} + 60q^{14} - 30q^{15} - 45q^{16} - 45q^{17} - 18q^{18} - 60q^{20} - 21q^{21} - 30q^{22} - 111q^{23} - 33q^{24} - 39q^{25} - 42q^{27} - 72q^{28} + 204q^{29} - 72q^{30} - 54q^{31} - 15q^{32} - 33q^{33} - 24q^{34} - 81q^{35} + 84q^{36} - 24q^{37} + 141q^{38} - 54q^{39} + 12q^{40} - 42q^{41} - 165q^{42} - 30q^{43} - 54q^{44} - 33q^{45} - 24q^{46} + 39q^{47} - 18q^{49} - 63q^{50} + 6q^{51} - 33q^{52} - 270q^{53} - 213q^{54} - 84q^{55} - 45q^{56} - 30q^{57} - 39q^{58} - 78q^{59} - 129q^{60} - 33q^{61} + 36q^{62} - 9q^{63} - 471q^{64} - 81q^{65} - 33q^{66} - 18q^{67} - 99q^{68} + 102q^{69} - 108q^{70} - 45q^{71} - 33q^{72} - 12q^{73} - 33q^{74} - 204q^{75} + 90q^{76} - 57q^{77} - 48q^{78} - 18q^{79} - 72q^{80} - 39q^{81} - 66q^{82} + 48q^{83} - 153q^{84} - 15q^{85} + 69q^{86} + 12q^{87} + 21q^{88} - 45q^{89} - 123q^{90} - 27q^{91} + 90q^{92} - 327q^{93} - 33q^{94} + 75q^{95} + 417q^{96} + 162q^{98} + O(q^{100})$$

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

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