# Properties

 Label 2366.2.bk Level $2366$ Weight $2$ Character orbit 2366.bk Rep. character $\chi_{2366}(53,\cdot)$ Character field $\Q(\zeta_{39})$ Dimension $2880$ Sturm bound $728$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2366 = 2 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2366.bk (of order $$39$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1183$$ Character field: $$\Q(\zeta_{39})$$ Sturm bound: $$728$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2366, [\chi])$$.

Total New Old
Modular forms 8832 2880 5952
Cusp forms 8640 2880 5760
Eisenstein series 192 0 192

## Trace form

 $$2880q + 120q^{4} - 8q^{7} + 124q^{9} + O(q^{10})$$ $$2880q + 120q^{4} - 8q^{7} + 124q^{9} + 4q^{10} + 4q^{11} - 48q^{13} + 4q^{14} + 72q^{15} + 120q^{16} + 8q^{17} - 4q^{19} + 16q^{21} + 8q^{23} + 112q^{25} - 6q^{26} + 4q^{28} - 16q^{29} - 44q^{30} + 12q^{31} - 28q^{33} - 248q^{36} + 12q^{38} - 52q^{39} + 4q^{40} + 32q^{41} + 20q^{42} - 40q^{43} + 4q^{44} + 40q^{45} + 4q^{46} + 12q^{47} + 44q^{49} - 48q^{50} + 24q^{51} - 2q^{52} - 116q^{53} + 66q^{54} + 24q^{55} - 8q^{56} - 48q^{57} - 28q^{58} + 8q^{59} + 16q^{60} - 12q^{61} - 8q^{62} - 126q^{63} - 240q^{64} - 4q^{65} + 16q^{66} + 60q^{67} + 8q^{68} + 40q^{69} - 200q^{70} - 148q^{71} + 4q^{73} - 104q^{74} - 214q^{75} - 44q^{76} - 52q^{77} + 28q^{79} + 152q^{81} - 8q^{82} + 24q^{83} - 32q^{84} + 176q^{85} + 74q^{86} - 16q^{87} - 28q^{89} - 40q^{90} + 120q^{91} - 16q^{92} - 20q^{93} - 20q^{94} - 112q^{95} - 188q^{97} + 24q^{98} - 40q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2366, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2366, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2366, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(1183, [\chi])$$$$^{\oplus 2}$$