# Properties

 Label 912.3 Level 912 Weight 3 Dimension 19180 Nonzero newspaces 24 Sturm bound 138240 Trace bound 13

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## Defining parameters

 Level: $$N$$ = $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$24$$ Sturm bound: $$138240$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(912))$$.

Total New Old
Modular forms 47088 19484 27604
Cusp forms 45072 19180 25892
Eisenstein series 2016 304 1712

## Trace form

 $$19180 q - 25 q^{3} - 88 q^{4} - 24 q^{5} - 44 q^{6} - 74 q^{7} + 24 q^{8} + 13 q^{9} + O(q^{10})$$ $$19180 q - 25 q^{3} - 88 q^{4} - 24 q^{5} - 44 q^{6} - 74 q^{7} + 24 q^{8} + 13 q^{9} + 88 q^{10} - 64 q^{11} + 76 q^{12} - 22 q^{13} + 88 q^{14} + 45 q^{15} - 104 q^{16} + 24 q^{17} + 60 q^{18} + 44 q^{19} - 160 q^{20} + 7 q^{21} - 216 q^{22} + 256 q^{23} + 4 q^{24} - 84 q^{25} + 200 q^{26} - 73 q^{27} - 72 q^{28} - 184 q^{29} - 348 q^{30} - 218 q^{31} - 320 q^{32} - 281 q^{33} - 536 q^{34} - 192 q^{35} - 452 q^{36} - 40 q^{37} - 168 q^{38} + 118 q^{39} - 344 q^{40} + 216 q^{41} - 476 q^{42} + 46 q^{43} - 176 q^{44} + 3 q^{45} + 56 q^{46} + 28 q^{48} - 176 q^{49} + 472 q^{50} - 283 q^{51} + 664 q^{52} + 392 q^{53} + 292 q^{54} + 330 q^{55} + 448 q^{56} + 41 q^{57} + 704 q^{58} + 256 q^{59} + 1260 q^{60} - 486 q^{61} + 552 q^{62} - 423 q^{63} + 1208 q^{64} - 1040 q^{65} + 964 q^{66} - 2418 q^{67} + 896 q^{68} - 501 q^{69} + 72 q^{70} - 1456 q^{71} + 468 q^{72} - 1014 q^{73} - 696 q^{74} - 936 q^{75} - 920 q^{76} - 592 q^{77} - 1300 q^{78} + 214 q^{79} - 1104 q^{80} - 51 q^{81} - 1464 q^{82} + 1184 q^{83} - 1940 q^{84} + 790 q^{85} - 1056 q^{86} + 1461 q^{87} - 1736 q^{88} + 1560 q^{89} - 2004 q^{90} + 2306 q^{91} - 992 q^{92} + 695 q^{93} - 24 q^{94} - 88 q^{96} + 90 q^{97} + 880 q^{98} + 493 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(912))$$

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
912.3.b $$\chi_{912}(911, \cdot)$$ 912.3.b.a 2 1
912.3.b.b 2
912.3.b.c 2
912.3.b.d 2
912.3.b.e 4
912.3.b.f 4
912.3.b.g 16
912.3.b.h 48
912.3.c $$\chi_{912}(343, \cdot)$$ None 0 1
912.3.h $$\chi_{912}(305, \cdot)$$ 912.3.h.a 12 1
912.3.h.b 12
912.3.h.c 12
912.3.h.d 36
912.3.i $$\chi_{912}(265, \cdot)$$ None 0 1
912.3.l $$\chi_{912}(455, \cdot)$$ None 0 1
912.3.m $$\chi_{912}(799, \cdot)$$ 912.3.m.a 12 1
912.3.m.b 12
912.3.m.c 12
912.3.n $$\chi_{912}(761, \cdot)$$ None 0 1
912.3.o $$\chi_{912}(721, \cdot)$$ 912.3.o.a 2 1
912.3.o.b 4
912.3.o.c 6
912.3.o.d 8
912.3.o.e 20
912.3.s $$\chi_{912}(77, \cdot)$$ n/a 576 2
912.3.t $$\chi_{912}(37, \cdot)$$ n/a 320 2
912.3.w $$\chi_{912}(227, \cdot)$$ n/a 632 2
912.3.x $$\chi_{912}(115, \cdot)$$ n/a 288 2
912.3.z $$\chi_{912}(463, \cdot)$$ 912.3.z.a 12 2
912.3.z.b 12
912.3.z.c 12
912.3.z.d 12
912.3.z.e 16
912.3.z.f 16
912.3.ba $$\chi_{912}(407, \cdot)$$ None 0 2
912.3.be $$\chi_{912}(145, \cdot)$$ 912.3.be.a 2 2
912.3.be.b 2
912.3.be.c 2
912.3.be.d 6
912.3.be.e 6
912.3.be.f 6
912.3.be.g 8
912.3.be.h 8
912.3.be.i 20
912.3.be.j 20
912.3.bf $$\chi_{912}(425, \cdot)$$ None 0 2
912.3.bi $$\chi_{912}(7, \cdot)$$ None 0 2
912.3.bj $$\chi_{912}(335, \cdot)$$ n/a 160 2
912.3.bk $$\chi_{912}(217, \cdot)$$ None 0 2
912.3.bl $$\chi_{912}(353, \cdot)$$ n/a 156 2
912.3.bp $$\chi_{912}(373, \cdot)$$ n/a 640 4
912.3.bs $$\chi_{912}(125, \cdot)$$ n/a 1264 4
912.3.bt $$\chi_{912}(163, \cdot)$$ n/a 640 4
912.3.bw $$\chi_{912}(107, \cdot)$$ n/a 1264 4
912.3.bx $$\chi_{912}(137, \cdot)$$ None 0 6
912.3.by $$\chi_{912}(97, \cdot)$$ n/a 240 6
912.3.cb $$\chi_{912}(17, \cdot)$$ n/a 468 6
912.3.cd $$\chi_{912}(409, \cdot)$$ None 0 6
912.3.ce $$\chi_{912}(143, \cdot)$$ n/a 480 6
912.3.cg $$\chi_{912}(55, \cdot)$$ None 0 6
912.3.cj $$\chi_{912}(71, \cdot)$$ None 0 6
912.3.cl $$\chi_{912}(175, \cdot)$$ n/a 240 6
912.3.cm $$\chi_{912}(59, \cdot)$$ n/a 3792 12
912.3.co $$\chi_{912}(43, \cdot)$$ n/a 1920 12
912.3.cr $$\chi_{912}(5, \cdot)$$ n/a 3792 12
912.3.ct $$\chi_{912}(13, \cdot)$$ n/a 1920 12

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(912))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(912)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 2}$$