# Properties

 Label 1216.4.cg Level $1216$ Weight $4$ Character orbit 1216.cg Rep. character $\chi_{1216}(5,\cdot)$ Character field $\Q(\zeta_{144})$ Dimension $22944$ Sturm bound $640$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1216.cg (of order $$144$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1216$$ Character field: $$\Q(\zeta_{144})$$ Sturm bound: $$640$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1216, [\chi])$$.

Total New Old
Modular forms 23136 23136 0
Cusp forms 22944 22944 0
Eisenstein series 192 192 0

## Trace form

 $$22944q - 48q^{2} - 48q^{3} - 48q^{4} - 48q^{5} - 48q^{6} - 24q^{7} - 24q^{8} - 48q^{9} + O(q^{10})$$ $$22944q - 48q^{2} - 48q^{3} - 48q^{4} - 48q^{5} - 48q^{6} - 24q^{7} - 24q^{8} - 48q^{9} - 48q^{10} - 24q^{11} - 24q^{12} - 48q^{13} - 48q^{14} - 48q^{15} - 48q^{16} - 48q^{17} - 96q^{18} - 48q^{19} - 96q^{20} - 48q^{21} - 48q^{22} - 48q^{23} - 48q^{24} - 48q^{25} - 24q^{26} - 24q^{27} - 48q^{28} - 48q^{29} - 24q^{30} - 48q^{32} - 6048q^{34} - 48q^{35} - 48q^{36} - 96q^{37} - 1368q^{38} - 96q^{39} - 4968q^{40} - 48q^{41} - 48q^{42} - 48q^{43} - 48q^{44} - 24q^{45} - 24q^{46} - 48q^{47} - 48q^{48} - 24q^{49} - 8592q^{50} - 8976q^{51} - 48q^{52} - 48q^{53} + 5136q^{54} - 48q^{55} - 96q^{56} - 48q^{57} - 96q^{58} - 48q^{59} - 48q^{60} - 48q^{61} - 240q^{62} - 96q^{63} - 24q^{64} - 48q^{65} - 48q^{66} - 48q^{67} - 6216q^{68} - 24q^{69} - 6096q^{70} - 48q^{71} - 48q^{72} - 48q^{73} - 48q^{74} - 96q^{75} - 48q^{76} - 96q^{77} - 48q^{78} - 48q^{79} - 48q^{80} - 48q^{81} - 48q^{82} - 24q^{83} - 24q^{84} - 48q^{85} - 48q^{86} - 24q^{87} - 24q^{88} - 48q^{89} + 28032q^{90} - 48q^{91} - 48q^{92} - 696q^{93} - 96q^{94} + 77424q^{96} - 48q^{98} - 48q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1216, [\chi])$$ into newform subspaces

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