## Defining parameters

 Level: $$N$$ = $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$24$$ Sturm bound: $$184320$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(912))$$.

Total New Old
Modular forms 70128 29152 40976
Cusp forms 68112 28844 39268
Eisenstein series 2016 308 1708

## Trace form

 $$28844 q - 17 q^{3} - 24 q^{4} - 4 q^{5} - 92 q^{6} - 102 q^{7} - 168 q^{8} - 123 q^{9} + O(q^{10})$$ $$28844 q - 17 q^{3} - 24 q^{4} - 4 q^{5} - 92 q^{6} - 102 q^{7} - 168 q^{8} - 123 q^{9} - 328 q^{10} + 120 q^{11} + 172 q^{12} - 62 q^{13} + 696 q^{14} - 327 q^{15} + 536 q^{16} + 52 q^{17} - 68 q^{18} - 86 q^{19} - 160 q^{20} + 475 q^{21} - 1400 q^{22} + 496 q^{23} - 252 q^{24} + 424 q^{25} + 40 q^{26} + 295 q^{27} + 1208 q^{28} - 116 q^{29} + 1444 q^{30} + 1386 q^{31} + 1920 q^{32} - 1201 q^{33} + 296 q^{34} - 240 q^{35} + 956 q^{36} - 2300 q^{37} - 1256 q^{38} - 1978 q^{39} - 4824 q^{40} - 828 q^{41} - 2748 q^{42} - 854 q^{43} + 400 q^{44} + 2727 q^{45} + 1464 q^{46} + 1152 q^{47} - 1380 q^{48} + 2684 q^{49} - 1416 q^{50} + 1137 q^{51} - 2728 q^{52} - 2468 q^{53} - 3436 q^{54} - 2550 q^{55} - 2688 q^{56} - 2289 q^{57} - 3168 q^{58} + 1256 q^{59} + 812 q^{60} + 11002 q^{61} + 1992 q^{62} + 1863 q^{63} + 4152 q^{64} + 4344 q^{65} + 4036 q^{66} + 8642 q^{67} + 3136 q^{68} + 5971 q^{69} + 13832 q^{70} - 3364 q^{71} + 8596 q^{72} - 5278 q^{73} + 5480 q^{74} - 12448 q^{75} + 2376 q^{76} - 21112 q^{77} + 6444 q^{78} - 27994 q^{79} - 1424 q^{80} - 811 q^{81} - 1528 q^{82} - 13788 q^{83} + 556 q^{84} - 8274 q^{85} + 3424 q^{86} + 1149 q^{87} - 9928 q^{88} + 15540 q^{89} - 6676 q^{90} + 32026 q^{91} - 10592 q^{92} + 14335 q^{93} - 21848 q^{94} + 10936 q^{95} - 21848 q^{96} + 1162 q^{97} - 13520 q^{98} - 1339 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(912))$$

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
912.4.a $$\chi_{912}(1, \cdot)$$ 912.4.a.a 1 1
912.4.a.b 1
912.4.a.c 1
912.4.a.d 1
912.4.a.e 1
912.4.a.f 1
912.4.a.g 1
912.4.a.h 1
912.4.a.i 2
912.4.a.j 2
912.4.a.k 2
912.4.a.l 2
912.4.a.m 2
912.4.a.n 2
912.4.a.o 3
912.4.a.p 3
912.4.a.q 3
912.4.a.r 4
912.4.a.s 4
912.4.a.t 4
912.4.a.u 4
912.4.a.v 4
912.4.a.w 5
912.4.d $$\chi_{912}(191, \cdot)$$ n/a 108 1
912.4.e $$\chi_{912}(151, \cdot)$$ None 0 1
912.4.f $$\chi_{912}(113, \cdot)$$ n/a 118 1
912.4.g $$\chi_{912}(457, \cdot)$$ None 0 1
912.4.j $$\chi_{912}(647, \cdot)$$ None 0 1
912.4.k $$\chi_{912}(607, \cdot)$$ 912.4.k.a 10 1
912.4.k.b 10
912.4.k.c 20
912.4.k.d 20
912.4.p $$\chi_{912}(569, \cdot)$$ None 0 1
912.4.q $$\chi_{912}(49, \cdot)$$ n/a 120 2
912.4.r $$\chi_{912}(341, \cdot)$$ n/a 952 2
912.4.u $$\chi_{912}(229, \cdot)$$ n/a 432 2
912.4.v $$\chi_{912}(419, \cdot)$$ n/a 864 2
912.4.y $$\chi_{912}(379, \cdot)$$ n/a 480 2
912.4.bb $$\chi_{912}(31, \cdot)$$ n/a 120 2
912.4.bc $$\chi_{912}(311, \cdot)$$ None 0 2
912.4.bd $$\chi_{912}(521, \cdot)$$ None 0 2
912.4.bg $$\chi_{912}(103, \cdot)$$ None 0 2
912.4.bh $$\chi_{912}(239, \cdot)$$ n/a 240 2
912.4.bm $$\chi_{912}(121, \cdot)$$ None 0 2
912.4.bn $$\chi_{912}(65, \cdot)$$ n/a 236 2
912.4.bo $$\chi_{912}(289, \cdot)$$ n/a 360 6
912.4.bq $$\chi_{912}(277, \cdot)$$ n/a 960 4
912.4.br $$\chi_{912}(221, \cdot)$$ n/a 1904 4
912.4.bu $$\chi_{912}(259, \cdot)$$ n/a 960 4
912.4.bv $$\chi_{912}(11, \cdot)$$ n/a 1904 4
912.4.bz $$\chi_{912}(41, \cdot)$$ None 0 6
912.4.ca $$\chi_{912}(25, \cdot)$$ None 0 6
912.4.cc $$\chi_{912}(257, \cdot)$$ n/a 708 6
912.4.cf $$\chi_{912}(295, \cdot)$$ None 0 6
912.4.ch $$\chi_{912}(47, \cdot)$$ n/a 720 6
912.4.ci $$\chi_{912}(79, \cdot)$$ n/a 360 6
912.4.ck $$\chi_{912}(23, \cdot)$$ None 0 6
912.4.cn $$\chi_{912}(67, \cdot)$$ n/a 2880 12
912.4.cp $$\chi_{912}(35, \cdot)$$ n/a 5712 12
912.4.cq $$\chi_{912}(61, \cdot)$$ n/a 2880 12
912.4.cs $$\chi_{912}(29, \cdot)$$ n/a 5712 12

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(912))$$ into lower level spaces

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