# Properties

 Label 912.6 Level 912 Weight 6 Dimension 48176 Nonzero newspaces 24 Sturm bound 276480 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$24$$ Sturm bound: $$276480$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(912))$$.

Total New Old
Modular forms 116208 48484 67724
Cusp forms 114192 48176 66016
Eisenstein series 2016 308 1708

## Trace form

 $$48176 q - 41 q^{3} - 152 q^{4} - 76 q^{5} + 196 q^{6} + 282 q^{7} + 984 q^{8} - 951 q^{9} + O(q^{10})$$ $$48176 q - 41 q^{3} - 152 q^{4} - 76 q^{5} + 196 q^{6} + 282 q^{7} + 984 q^{8} - 951 q^{9} - 1800 q^{10} - 3624 q^{11} - 20 q^{12} + 394 q^{13} - 648 q^{14} + 4473 q^{15} - 8424 q^{16} - 404 q^{17} + 8764 q^{18} - 9734 q^{19} + 15200 q^{20} - 3989 q^{21} - 2488 q^{22} + 9328 q^{23} - 15612 q^{24} + 3892 q^{25} + 25960 q^{26} + 5983 q^{27} + 3768 q^{28} + 16708 q^{29} + 1444 q^{30} - 40726 q^{31} - 88320 q^{32} - 15265 q^{33} - 62296 q^{34} + 38352 q^{35} + 64700 q^{36} + 25420 q^{37} + 72088 q^{38} + 80294 q^{39} + 180776 q^{40} + 21756 q^{41} + 5892 q^{42} - 44406 q^{43} - 87536 q^{44} - 65121 q^{45} - 244040 q^{46} - 70272 q^{47} - 71268 q^{48} - 162112 q^{49} - 212424 q^{50} - 59007 q^{51} + 329688 q^{52} + 223636 q^{53} + 68084 q^{54} + 198026 q^{55} + 317184 q^{56} + 42591 q^{57} + 70624 q^{58} + 61064 q^{59} + 71852 q^{60} + 337074 q^{61} - 382200 q^{62} - 82809 q^{63} - 715976 q^{64} - 820152 q^{65} - 310460 q^{66} - 1327614 q^{67} + 244672 q^{68} - 304061 q^{69} + 747912 q^{70} + 143228 q^{71} + 90388 q^{72} + 694970 q^{73} + 189992 q^{74} + 865856 q^{75} - 242296 q^{76} + 1014488 q^{77} - 426324 q^{78} + 1096422 q^{79} - 1246736 q^{80} + 997001 q^{81} + 333704 q^{82} - 244908 q^{83} + 10156 q^{84} - 376898 q^{85} + 1162336 q^{86} - 1252995 q^{87} + 1179960 q^{88} - 673716 q^{89} + 127340 q^{90} - 259878 q^{91} + 25504 q^{92} - 155609 q^{93} - 1021912 q^{94} - 119624 q^{95} + 19624 q^{96} - 1038990 q^{97} - 955472 q^{98} + 282149 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(912))$$

We only show spaces with even 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
912.6.a $$\chi_{912}(1, \cdot)$$ 912.6.a.a 1 1
912.6.a.b 1
912.6.a.c 1
912.6.a.d 1
912.6.a.e 1
912.6.a.f 1
912.6.a.g 2
912.6.a.h 2
912.6.a.i 2
912.6.a.j 2
912.6.a.k 3
912.6.a.l 3
912.6.a.m 3
912.6.a.n 3
912.6.a.o 3
912.6.a.p 4
912.6.a.q 4
912.6.a.r 4
912.6.a.s 4
912.6.a.t 5
912.6.a.u 5
912.6.a.v 5
912.6.a.w 5
912.6.a.x 5
912.6.a.y 6
912.6.a.z 7
912.6.a.ba 7
912.6.d $$\chi_{912}(191, \cdot)$$ n/a 180 1
912.6.e $$\chi_{912}(151, \cdot)$$ None 0 1
912.6.f $$\chi_{912}(113, \cdot)$$ n/a 198 1
912.6.g $$\chi_{912}(457, \cdot)$$ None 0 1
912.6.j $$\chi_{912}(647, \cdot)$$ None 0 1
912.6.k $$\chi_{912}(607, \cdot)$$ 912.6.k.a 16 1
912.6.k.b 16
912.6.k.c 34
912.6.k.d 34
912.6.p $$\chi_{912}(569, \cdot)$$ None 0 1
912.6.q $$\chi_{912}(49, \cdot)$$ n/a 200 2
912.6.r $$\chi_{912}(341, \cdot)$$ n/a 1592 2
912.6.u $$\chi_{912}(229, \cdot)$$ n/a 720 2
912.6.v $$\chi_{912}(419, \cdot)$$ n/a 1440 2
912.6.y $$\chi_{912}(379, \cdot)$$ n/a 800 2
912.6.bb $$\chi_{912}(31, \cdot)$$ n/a 200 2
912.6.bc $$\chi_{912}(311, \cdot)$$ None 0 2
912.6.bd $$\chi_{912}(521, \cdot)$$ None 0 2
912.6.bg $$\chi_{912}(103, \cdot)$$ None 0 2
912.6.bh $$\chi_{912}(239, \cdot)$$ n/a 400 2
912.6.bm $$\chi_{912}(121, \cdot)$$ None 0 2
912.6.bn $$\chi_{912}(65, \cdot)$$ n/a 396 2
912.6.bo $$\chi_{912}(289, \cdot)$$ n/a 600 6
912.6.bq $$\chi_{912}(277, \cdot)$$ n/a 1600 4
912.6.br $$\chi_{912}(221, \cdot)$$ n/a 3184 4
912.6.bu $$\chi_{912}(259, \cdot)$$ n/a 1600 4
912.6.bv $$\chi_{912}(11, \cdot)$$ n/a 3184 4
912.6.bz $$\chi_{912}(41, \cdot)$$ None 0 6
912.6.ca $$\chi_{912}(25, \cdot)$$ None 0 6
912.6.cc $$\chi_{912}(257, \cdot)$$ n/a 1188 6
912.6.cf $$\chi_{912}(295, \cdot)$$ None 0 6
912.6.ch $$\chi_{912}(47, \cdot)$$ n/a 1200 6
912.6.ci $$\chi_{912}(79, \cdot)$$ n/a 600 6
912.6.ck $$\chi_{912}(23, \cdot)$$ None 0 6
912.6.cn $$\chi_{912}(67, \cdot)$$ n/a 4800 12
912.6.cp $$\chi_{912}(35, \cdot)$$ n/a 9552 12
912.6.cq $$\chi_{912}(61, \cdot)$$ n/a 4800 12
912.6.cs $$\chi_{912}(29, \cdot)$$ n/a 9552 12

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(912))$$ into lower level spaces

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