# Properties

 Label 1323.2.bl Level $1323$ Weight $2$ Character orbit 1323.bl Rep. character $\chi_{1323}(100,\cdot)$ 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.bl (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

 $$648q + 8q^{2} + 44q^{4} - 3q^{5} - 7q^{7} + 16q^{8} + O(q^{10})$$ $$648q + 8q^{2} + 44q^{4} - 3q^{5} - 7q^{7} + 16q^{8} - 22q^{10} + 5q^{11} - 4q^{13} - 52q^{14} + 38q^{16} + 37q^{17} - 14q^{19} + 11q^{20} - q^{22} + 20q^{23} - 97q^{25} + 44q^{26} - 22q^{28} + 53q^{29} + 10q^{31} + 10q^{32} - 7q^{34} + 32q^{35} - 39q^{37} - 59q^{38} - 19q^{40} + 17q^{41} - q^{43} + 31q^{44} + 56q^{46} - 50q^{47} - 19q^{49} + 21q^{50} - 9q^{52} - 50q^{53} + 20q^{55} + 239q^{56} + 17q^{58} + 37q^{59} - 105q^{61} + 30q^{62} - 88q^{64} + 5q^{65} + 13q^{67} + 290q^{68} + 17q^{70} + 19q^{71} - 40q^{73} + 57q^{74} - 41q^{76} - 19q^{77} + 13q^{79} - 163q^{80} - 28q^{82} - 73q^{83} - 10q^{85} - 15q^{86} - 13q^{88} + 104q^{89} - 49q^{91} + 91q^{92} - 4q^{94} + 29q^{95} - 11q^{97} + 33q^{98} + O(q^{100})$$

## 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

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