# Properties

 Label 63.4.i Level $63$ Weight $4$ Character orbit 63.i Rep. character $\chi_{63}(5,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $44$ Newform subspaces $1$ Sturm bound $32$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 63.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(63, [\chi])$$.

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

## Trace form

 $$44q - 3q^{3} - 162q^{4} - 3q^{5} + 24q^{6} + 5q^{7} - 45q^{9} + O(q^{10})$$ $$44q - 3q^{3} - 162q^{4} - 3q^{5} + 24q^{6} + 5q^{7} - 45q^{9} - 6q^{10} + 9q^{11} + 186q^{12} - 36q^{13} + 54q^{14} - 141q^{15} + 526q^{16} - 72q^{17} - 54q^{18} - 6q^{19} + 24q^{20} - 81q^{21} + 14q^{22} - 285q^{23} - 114q^{24} - 349q^{25} - 96q^{26} + 432q^{27} - 156q^{28} - 132q^{29} - 447q^{30} - 3q^{33} + 24q^{34} + 765q^{35} + 1122q^{36} + 82q^{37} - 873q^{38} + 306q^{39} + 420q^{40} + 618q^{41} - 282q^{42} + 82q^{43} + 603q^{44} + 291q^{45} + 266q^{46} - 402q^{47} - 1569q^{48} - 79q^{49} - 1845q^{50} + 453q^{51} + 189q^{52} + 564q^{53} - 2385q^{54} + 66q^{56} + 1170q^{57} + 269q^{58} + 1494q^{59} + 2265q^{60} - 2904q^{62} - 636q^{63} - 1144q^{64} - 372q^{66} - 590q^{67} + 3504q^{68} - 1005q^{69} - 105q^{70} + 1830q^{72} - 6q^{73} + 1515q^{74} - 33q^{75} - 144q^{76} - 4443q^{77} - 5985q^{78} + 1102q^{79} - 4239q^{80} - 4017q^{81} + 18q^{82} + 1830q^{83} + 3165q^{84} - 237q^{85} + 1209q^{86} + 2013q^{87} - 623q^{88} + 4266q^{89} + 9993q^{90} - 1140q^{91} + 7896q^{92} - 729q^{93} + 3975q^{96} - 792q^{97} + 5667q^{98} + 4335q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(63, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
63.4.i.a $$44$$ $$3.717$$ None $$0$$ $$-3$$ $$-3$$ $$5$$