# Properties

 Label 1323.2.cc Level $1323$ Weight $2$ Character orbit 1323.cc Rep. character $\chi_{1323}(4,\cdot)$ Character field $\Q(\zeta_{63})$ Dimension $5976$ Sturm bound $336$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.cc (of order $$63$$ and degree $$36$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1323$$ Character field: $$\Q(\zeta_{63})$$ 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

 $$5976q - 39q^{2} - 39q^{3} - 39q^{4} - 39q^{5} - 108q^{6} - 36q^{7} - 15q^{8} - 39q^{9} + O(q^{10})$$ $$5976q - 39q^{2} - 39q^{3} - 39q^{4} - 39q^{5} - 108q^{6} - 36q^{7} - 15q^{8} - 39q^{9} - 24q^{10} - 39q^{11} - 39q^{12} - 30q^{13} - 222q^{14} - 30q^{15} - 51q^{16} - 48q^{17} - 18q^{18} + 18q^{19} - 24q^{20} - 57q^{21} - 30q^{22} + 33q^{23} + 30q^{24} - 39q^{25} - 114q^{26} - 30q^{27} - 72q^{28} + 114q^{29} - 18q^{30} - 18q^{31} - 27q^{32} - 57q^{33} - 24q^{34} - 36q^{35} - 234q^{36} - 15q^{37} - 69q^{38} - 69q^{39} - 93q^{40} - 42q^{41} - 339q^{42} - 30q^{43} - 15q^{44} - 21q^{45} - 15q^{46} + 105q^{47} - 174q^{48} - 33q^{50} - 75q^{51} - 51q^{52} - 198q^{53} - 33q^{54} - 60q^{55} - 153q^{56} + 114q^{57} - 39q^{58} - 69q^{59} - 39q^{60} - 21q^{61} - 96q^{62} - 105q^{63} + 441q^{64} - 18q^{65} - 39q^{66} - 18q^{67} + 9q^{68} - 540q^{69} - 81q^{70} - 15q^{71} - 147q^{72} + 21q^{73} - 51q^{74} - 249q^{75} + 66q^{76} - 57q^{77} - 48q^{78} - 18q^{79} + 444q^{80} - 39q^{81} - 78q^{82} + 54q^{84} - 15q^{85} + 15q^{86} - 117q^{87} + 9q^{88} - 96q^{89} - 3q^{90} + 162q^{92} + 141q^{93} - 75q^{94} + 72q^{95} - 627q^{96} - 72q^{97} + 183q^{98} - 288q^{99} + O(q^{100})$$

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

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