# Properties

 Label 126.3 Level 126 Weight 3 Dimension 216 Nonzero newspaces 10 Newform subspaces 14 Sturm bound 2592 Trace bound 9

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## Defining parameters

 Level: $$N$$ = $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$10$$ Newform subspaces: $$14$$ Sturm bound: $$2592$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(126))$$.

Total New Old
Modular forms 960 216 744
Cusp forms 768 216 552
Eisenstein series 192 0 192

## Trace form

 $$216 q - 4 q^{4} + 30 q^{5} + 24 q^{6} + 14 q^{7} - 24 q^{9} + O(q^{10})$$ $$216 q - 4 q^{4} + 30 q^{5} + 24 q^{6} + 14 q^{7} - 24 q^{9} - 18 q^{11} - 24 q^{12} + 44 q^{13} + 72 q^{14} + 84 q^{15} + 24 q^{16} + 186 q^{17} + 96 q^{18} + 206 q^{19} + 72 q^{20} + 6 q^{21} + 48 q^{22} - 222 q^{23} - 48 q^{24} - 312 q^{25} - 264 q^{26} - 252 q^{27} - 108 q^{28} - 420 q^{29} - 264 q^{30} - 142 q^{31} + 84 q^{33} - 120 q^{34} + 390 q^{35} - 24 q^{36} + 10 q^{37} + 132 q^{38} + 276 q^{39} + 252 q^{41} + 48 q^{42} + 148 q^{43} + 36 q^{44} - 84 q^{45} - 12 q^{46} - 366 q^{47} - 48 q^{48} - 66 q^{49} - 384 q^{50} - 1008 q^{51} + 152 q^{52} - 1194 q^{53} - 648 q^{54} - 72 q^{55} - 24 q^{56} - 768 q^{57} + 240 q^{58} - 510 q^{59} - 72 q^{60} - 274 q^{61} - 54 q^{63} + 128 q^{64} - 12 q^{65} + 528 q^{66} - 210 q^{67} + 132 q^{68} + 972 q^{69} - 240 q^{70} + 984 q^{71} + 192 q^{72} + 350 q^{73} + 384 q^{74} + 1872 q^{75} - 328 q^{76} + 1044 q^{77} + 480 q^{78} + 270 q^{79} + 24 q^{80} + 528 q^{81} - 144 q^{82} + 756 q^{83} + 144 q^{84} - 132 q^{85} + 672 q^{86} + 576 q^{87} + 120 q^{88} + 1278 q^{89} + 672 q^{90} + 476 q^{91} + 384 q^{92} + 240 q^{93} + 300 q^{94} + 474 q^{95} + 164 q^{97} + 744 q^{98} - 156 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(126))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
126.3.b $$\chi_{126}(71, \cdot)$$ 126.3.b.a 4 1
126.3.c $$\chi_{126}(55, \cdot)$$ 126.3.c.a 4 1
126.3.c.b 4
126.3.i $$\chi_{126}(65, \cdot)$$ 126.3.i.a 32 2
126.3.j $$\chi_{126}(31, \cdot)$$ 126.3.j.a 32 2
126.3.n $$\chi_{126}(19, \cdot)$$ 126.3.n.a 4 2
126.3.n.b 4
126.3.n.c 4
126.3.o $$\chi_{126}(13, \cdot)$$ 126.3.o.a 32 2
126.3.p $$\chi_{126}(103, \cdot)$$ 126.3.p.a 32 2
126.3.q $$\chi_{126}(29, \cdot)$$ 126.3.q.a 24 2
126.3.r $$\chi_{126}(11, \cdot)$$ 126.3.r.a 32 2
126.3.s $$\chi_{126}(53, \cdot)$$ 126.3.s.a 4 2
126.3.s.b 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(126))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(126)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$