# Properties

 Label 1323.2.ca Level $1323$ Weight $2$ Character orbit 1323.ca Rep. character $\chi_{1323}(25,\cdot)$ Character field $\Q(\zeta_{63})$ Dimension $5976$ Sturm bound $336$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.ca (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

 $$5976q - 39q^{2} - 39q^{3} - 39q^{4} - 39q^{5} + 18q^{6} - 36q^{7} - 15q^{8} - 39q^{9} + O(q^{10})$$ $$5976q - 39q^{2} - 39q^{3} - 39q^{4} - 39q^{5} + 18q^{6} - 36q^{7} - 15q^{8} - 39q^{9} - 15q^{10} - 39q^{11} - 39q^{12} - 30q^{13} + 48q^{14} - 30q^{15} - 33q^{16} + 33q^{17} - 18q^{18} - 36q^{19} - 24q^{20} - 21q^{21} - 30q^{22} + 33q^{23} - 87q^{24} - 39q^{25} - 114q^{26} - 30q^{27} - 72q^{28} - 264q^{29} + 36q^{30} - 18q^{31} - 63q^{32} - 57q^{33} - 24q^{34} - 9q^{35} + 144q^{36} - 24q^{37} - 69q^{38} - 24q^{39} + 24q^{40} - 42q^{41} + 93q^{42} - 30q^{43} - 24q^{44} - 75q^{45} - 24q^{46} + 105q^{47} - 174q^{48} - 54q^{49} - 33q^{50} + 6q^{51} - 51q^{52} - 198q^{53} + 21q^{54} - 60q^{55} - 99q^{56} - 264q^{57} - 39q^{58} - 24q^{59} - 93q^{60} - 75q^{61} - 96q^{62} - 105q^{63} + 441q^{64} - 81q^{65} - 111q^{66} - 18q^{67} - 27q^{68} + 216q^{69} - 15q^{71} + 15q^{72} - 42q^{73} - 33q^{74} + 66q^{75} - 186q^{76} - 129q^{77} - 48q^{78} - 18q^{79} + 444q^{80} - 39q^{81} - 78q^{82} + 225q^{84} - 15q^{85} - 147q^{86} - 72q^{87} - 99q^{88} + 129q^{89} - 3q^{90} - 27q^{91} + 162q^{92} + 249q^{93} - 75q^{94} - 153q^{95} + 255q^{96} - 72q^{97} - 204q^{98} - 288q^{99} + O(q^{100})$$

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

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