# Properties

 Label 126.9 Level 126 Weight 9 Dimension 872 Nonzero newspaces 10 Sturm bound 7776 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$9$$ Nonzero newspaces: $$10$$ Sturm bound: $$7776$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(\Gamma_1(126))$$.

Total New Old
Modular forms 3552 872 2680
Cusp forms 3360 872 2488
Eisenstein series 192 0 192

## Trace form

 $$872 q - 252 q^{3} - 1280 q^{4} + 3438 q^{5} - 768 q^{6} - 1778 q^{7} + 57324 q^{9} + O(q^{10})$$ $$872 q - 252 q^{3} - 1280 q^{4} + 3438 q^{5} - 768 q^{6} - 1778 q^{7} + 57324 q^{9} - 13056 q^{10} - 94770 q^{11} - 10752 q^{12} + 234828 q^{13} - 188928 q^{14} - 2508 q^{15} + 229376 q^{16} - 80622 q^{17} - 104448 q^{18} - 539094 q^{19} + 225792 q^{20} + 1478490 q^{21} + 407808 q^{22} - 871902 q^{23} + 98304 q^{24} - 3825220 q^{25} - 3091968 q^{26} - 1388268 q^{27} - 272128 q^{28} + 13120596 q^{29} + 3466752 q^{30} - 8670186 q^{31} - 6916776 q^{33} - 1141248 q^{34} + 12079674 q^{35} + 7311360 q^{36} - 5976994 q^{37} + 3907584 q^{38} - 1176348 q^{39} + 1671168 q^{40} - 18437184 q^{41} - 14237952 q^{42} - 16466320 q^{43} - 417024 q^{44} + 85741764 q^{45} + 15773184 q^{46} + 61937190 q^{47} + 2752512 q^{48} - 73961422 q^{49} - 16676352 q^{50} - 32650812 q^{51} + 2374656 q^{52} - 31312782 q^{53} - 87443712 q^{54} + 49393080 q^{55} + 21233664 q^{56} + 128890356 q^{57} - 20613120 q^{58} - 60173730 q^{59} + 67290624 q^{60} - 151424478 q^{61} - 147383766 q^{63} + 117440512 q^{64} + 5962320 q^{65} - 140957184 q^{66} + 29609098 q^{67} - 27456768 q^{68} - 81312012 q^{69} - 95052288 q^{70} + 263690352 q^{71} + 23789568 q^{72} + 165712794 q^{73} - 15471360 q^{74} - 456283908 q^{75} - 71233536 q^{76} - 396289116 q^{77} - 212531712 q^{78} - 458555738 q^{79} - 27426816 q^{80} + 47131404 q^{81} + 149422080 q^{82} - 228400452 q^{83} + 15040512 q^{84} + 976322172 q^{85} + 948093696 q^{86} + 408124152 q^{87} + 4718592 q^{88} - 741961062 q^{89} - 430920192 q^{90} - 819209244 q^{91} - 137622528 q^{92} + 339364032 q^{93} + 438787584 q^{94} + 868610466 q^{95} + 75497472 q^{96} - 14874456 q^{97} - 640115712 q^{98} - 1229678004 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(\Gamma_1(126))$$

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
126.9.b $$\chi_{126}(71, \cdot)$$ 126.9.b.a 8 1
126.9.b.b 8
126.9.c $$\chi_{126}(55, \cdot)$$ 126.9.c.a 4 1
126.9.c.b 12
126.9.c.c 12
126.9.i $$\chi_{126}(65, \cdot)$$ n/a 128 2
126.9.j $$\chi_{126}(31, \cdot)$$ n/a 128 2
126.9.n $$\chi_{126}(19, \cdot)$$ 126.9.n.a 8 2
126.9.n.b 12
126.9.n.c 12
126.9.n.d 20
126.9.o $$\chi_{126}(13, \cdot)$$ n/a 128 2
126.9.p $$\chi_{126}(103, \cdot)$$ n/a 128 2
126.9.q $$\chi_{126}(29, \cdot)$$ 126.9.q.a 96 2
126.9.r $$\chi_{126}(11, \cdot)$$ n/a 128 2
126.9.s $$\chi_{126}(53, \cdot)$$ 126.9.s.a 20 2
126.9.s.b 20

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{9}^{\mathrm{old}}(\Gamma_1(126))$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(\Gamma_1(126)) \cong$$ $$S_{9}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$