# Properties

 Label 1323.2.bk Level $1323$ Weight $2$ Character orbit 1323.bk Rep. character $\chi_{1323}(37,\cdot)$ Character field $\Q(\zeta_{21})$ Dimension $648$ Sturm bound $336$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.bk (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$441$$ Character field: $$\Q(\zeta_{21})$$ Sturm bound: $$336$$

## Dimensions

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

Total New Old
Modular forms 2088 696 1392
Cusp forms 1944 648 1296
Eisenstein series 144 48 96

## Trace form

 $$648q + 5q^{2} - 109q^{4} + 12q^{5} - 7q^{7} + 16q^{8} + O(q^{10})$$ $$648q + 5q^{2} - 109q^{4} + 12q^{5} - 7q^{7} + 16q^{8} - 22q^{10} + 8q^{11} - 4q^{13} + 26q^{14} - 97q^{16} + 37q^{17} - 14q^{19} + 11q^{20} - q^{22} - 31q^{23} + 38q^{25} + 44q^{26} - 22q^{28} - 73q^{29} - 20q^{31} + q^{32} - 7q^{34} + 32q^{35} - 39q^{37} + 40q^{38} - q^{40} + 17q^{41} - q^{43} + 31q^{44} + 56q^{46} - 5q^{47} - q^{49} + 21q^{50} - 48q^{52} - 50q^{53} + 20q^{55} - 127q^{56} - 82q^{58} - 53q^{59} + 42q^{61} + 30q^{62} - 88q^{64} + 11q^{65} - 26q^{67} - 145q^{68} - 46q^{70} + 19q^{71} - 40q^{73} - 18q^{74} + 43q^{76} - 7q^{77} - 26q^{79} - 163q^{80} - 28q^{82} + 221q^{83} - 10q^{85} + 18q^{86} - 4q^{88} + 104q^{89} - 49q^{91} - 119q^{92} - 13q^{94} - 37q^{95} - 11q^{97} + 33q^{98} + O(q^{100})$$

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

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1323, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1323, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$