# Properties

 Label 126.3.j Level $126$ Weight $3$ Character orbit 126.j Rep. character $\chi_{126}(31,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $1$ Sturm bound $72$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 126.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$72$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(126, [\chi])$$.

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

## Trace form

 $$32 q - 32 q^{4} - 2 q^{7} - 12 q^{9} + O(q^{10})$$ $$32 q - 32 q^{4} - 2 q^{7} - 12 q^{9} + 24 q^{11} - 30 q^{13} - 12 q^{14} + 30 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 84 q^{23} - 24 q^{24} - 160 q^{25} - 72 q^{26} + 126 q^{27} - 4 q^{28} - 84 q^{29} - 24 q^{31} + 126 q^{33} - 66 q^{35} + 24 q^{36} - 22 q^{37} + 186 q^{39} + 396 q^{41} + 24 q^{42} - 16 q^{43} - 24 q^{44} - 258 q^{45} + 12 q^{46} + 108 q^{47} - 22 q^{49} - 96 q^{50} - 150 q^{51} - 252 q^{53} - 144 q^{54} + 48 q^{56} - 318 q^{57} + 48 q^{58} - 90 q^{59} - 108 q^{60} - 102 q^{61} + 246 q^{63} + 256 q^{64} - 6 q^{65} + 336 q^{66} + 70 q^{67} - 210 q^{69} - 108 q^{70} + 300 q^{71} - 48 q^{72} + 144 q^{74} + 390 q^{75} - 114 q^{77} + 96 q^{78} + 106 q^{79} - 144 q^{81} - 756 q^{83} - 72 q^{84} - 60 q^{85} + 240 q^{86} + 258 q^{87} + 414 q^{89} + 360 q^{90} - 186 q^{91} - 84 q^{92} - 222 q^{93} - 552 q^{95} + 48 q^{96} + 114 q^{97} - 96 q^{98} + 90 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(126, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.j.a $32$ $3.433$ None $$0$$ $$0$$ $$0$$ $$-2$$

## Decomposition of $$S_{3}^{\mathrm{old}}(126, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(126, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$