# Properties

 Label 72.22.n Level $72$ Weight $22$ Character orbit 72.n Rep. character $\chi_{72}(13,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $500$ Sturm bound $264$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$22$$ Character orbit: $$[\chi]$$ $$=$$ 72.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$72$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$264$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{22}(72, [\chi])$$.

Total New Old
Modular forms 508 508 0
Cusp forms 500 500 0
Eisenstein series 8 8 0

## Trace form

 $$500 q - q^{2} - q^{4} - 73477609 q^{6} - 2 q^{7} - 5141984986 q^{8} - 4 q^{9} + O(q^{10})$$ $$500 q - q^{2} - q^{4} - 73477609 q^{6} - 2 q^{7} - 5141984986 q^{8} - 4 q^{9} - 4194308 q^{10} + 483747918716 q^{12} - 1141577578522 q^{14} - 20920706410 q^{15} - q^{16} - 8 q^{17} - 23272689749042 q^{18} - 56112703368676 q^{20} - 4194305 q^{22} - 497118134563790 q^{23} + 80484599973715 q^{24} + 23078918457031248 q^{25} - 359200175997952 q^{26} + 8796093022204 q^{28} - 13863913176661862 q^{30} - 2 q^{31} + 25907817264286579 q^{32} + 10718163280653294 q^{33} + 2860283538034821 q^{34} - 62136869208192021 q^{36} + 16034625630817735 q^{38} - 56620661393812510 q^{39} + 43541998349609374 q^{40} - 41675527200818542 q^{41} + 532384929881573642 q^{42} - 1135314426846330150 q^{44} - 226626385809914952 q^{46} + 1051982644716600978 q^{47} + 631664483577943911 q^{48} - 18990559378831656240 q^{49} + 1154261627550639845 q^{50} + 147743479683087324 q^{52} - 3424002596437638563 q^{54} - 1907348632812508 q^{55} + 1676432816364030986 q^{56} + 1689283534795301812 q^{57} - 3029449227257522096 q^{58} - 3353248314639683358 q^{60} - 24221677513544225264 q^{62} + 5487979692052415090 q^{63} - 41625993542941193062 q^{64} - 1907348632812502 q^{65} - 83892328349702988054 q^{66} - 27416007966946304667 q^{68} - 559499538397593106 q^{70} + 182293638856553347248 q^{71} - 174647360632917828233 q^{72} - 8 q^{73} - 94759239753964700950 q^{74} + 22082012104852762029 q^{76} + 43396208542644430318 q^{78} - 2 q^{79} + 183811678890187754688 q^{80} + 144600177197346839848 q^{81} + 129661334539001624586 q^{82} - 334867374179979938980 q^{84} - 842471176944215835547 q^{86} - 1855868405261351355894 q^{87} + 155086103622875112619 q^{88} + 458536208803779654728 q^{89} + 646868699260111508464 q^{90} + 2451498732058471342302 q^{92} - 1091329553602604696034 q^{94} + 1915959159237128906248 q^{95} + 2075402397269645161174 q^{96} - 2 q^{97} - 10898446915317364803150 q^{98} + O(q^{100})$$

## Decomposition of $$S_{22}^{\mathrm{new}}(72, [\chi])$$ into newform subspaces

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