# Properties

 Label 171.3.z Level $171$ Weight $3$ Character orbit 171.z Rep. character $\chi_{171}(5,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $228$ Newform subspaces $1$ Sturm bound $60$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$171 = 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 171.z (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$171$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(171, [\chi])$$.

Total New Old
Modular forms 252 252 0
Cusp forms 228 228 0
Eisenstein series 24 24 0

## Trace form

 $$228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} + O(q^{10})$$ $$228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21} + 81 q^{22} + 207 q^{23} - 222 q^{24} - 3 q^{25} - 216 q^{26} - 33 q^{27} - 36 q^{28} - 9 q^{29} + 171 q^{30} - 6 q^{31} - 9 q^{32} + 30 q^{33} + 33 q^{34} + 225 q^{35} - 246 q^{36} - 24 q^{37} - 9 q^{38} - 60 q^{39} - 177 q^{40} - 9 q^{41} - 15 q^{42} + 93 q^{43} + 441 q^{44} - 57 q^{45} - 6 q^{46} - 9 q^{47} - 774 q^{48} - 543 q^{49} - 81 q^{51} + 213 q^{52} + 393 q^{54} + 63 q^{55} - 459 q^{56} + 84 q^{57} - 6 q^{58} + 126 q^{59} - 333 q^{60} - 24 q^{61} - 36 q^{62} + 369 q^{63} + 372 q^{64} + 894 q^{66} + 39 q^{67} + 747 q^{68} + 231 q^{69} + 291 q^{70} + 204 q^{72} - 51 q^{73} + 333 q^{74} + 324 q^{75} - 3 q^{76} - 18 q^{77} - 1569 q^{78} - 105 q^{79} - 756 q^{80} + 1050 q^{81} + 132 q^{82} + 99 q^{83} - 69 q^{84} - 3 q^{85} - 495 q^{86} - 483 q^{87} + 387 q^{88} - 648 q^{89} - 339 q^{90} + 225 q^{91} + 27 q^{92} + 396 q^{93} - 6 q^{94} - 1305 q^{95} - 663 q^{96} - 543 q^{97} + 1125 q^{98} - 300 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(171, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.3.z.a $228$ $4.659$ None $$-9$$ $$6$$ $$-9$$ $$3$$