# Properties

 Label 63.3.j Level $63$ Weight $3$ Character orbit 63.j Rep. character $\chi_{63}(11,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $28$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 63.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(63, [\chi])$$.

Total New Old
Modular forms 36 36 0
Cusp forms 28 28 0
Eisenstein series 8 8 0

## Trace form

 $$28 q - q^{3} - 50 q^{4} - 3 q^{5} - 8 q^{6} - 2 q^{7} + 17 q^{9} + O(q^{10})$$ $$28 q - q^{3} - 50 q^{4} - 3 q^{5} - 8 q^{6} - 2 q^{7} + 17 q^{9} + 6 q^{10} + 15 q^{11} - 38 q^{12} - 7 q^{13} - 84 q^{14} + 8 q^{15} + 70 q^{16} + 27 q^{17} + 40 q^{18} - 16 q^{19} + 6 q^{20} - 17 q^{21} + 6 q^{22} + 96 q^{23} + 126 q^{24} + 31 q^{25} + 84 q^{26} + 65 q^{27} - 8 q^{28} - 114 q^{29} - 95 q^{30} - 34 q^{31} - 31 q^{33} - 6 q^{34} - 30 q^{35} - 158 q^{36} - 13 q^{37} - 69 q^{38} - 43 q^{39} - 48 q^{40} - 78 q^{41} - 4 q^{42} - 34 q^{43} - 327 q^{44} - 349 q^{45} + 18 q^{46} + 169 q^{48} + 10 q^{49} + 357 q^{50} + 240 q^{51} + 17 q^{52} + 108 q^{53} + 433 q^{54} + 66 q^{55} + 552 q^{56} + 167 q^{57} + 33 q^{58} - 347 q^{60} - 112 q^{61} + q^{63} - 32 q^{64} + 256 q^{66} + 68 q^{67} - 540 q^{68} - 252 q^{69} - 21 q^{70} - 222 q^{72} - 100 q^{73} - 69 q^{74} - 374 q^{75} + 134 q^{76} - 426 q^{77} - 197 q^{78} - 100 q^{79} - 3 q^{80} + 317 q^{81} - 6 q^{82} + 354 q^{83} - 139 q^{84} - 57 q^{85} + 753 q^{86} + 551 q^{87} - 87 q^{88} + 477 q^{89} + 247 q^{90} + 107 q^{91} - 1092 q^{92} - 312 q^{93} + 366 q^{94} - 397 q^{96} + 17 q^{97} - 123 q^{98} - 184 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(63, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.3.j.a $6$ $1.717$ 6.0.63369648.1 None $$0$$ $$18$$ $$-15$$ $$-2$$ $$q+(-1-\beta _{4}-\beta _{5})q^{2}+3q^{3}+(-4+\cdots)q^{4}+\cdots$$
63.3.j.b $22$ $1.717$ None $$0$$ $$-19$$ $$12$$ $$0$$