Properties

 Label 3192.2 Level 3192 Weight 2 Dimension 110480 Nonzero newspaces 96 Sturm bound 1105920 Trace bound 28

Defining parameters

 Level: $$N$$ = $$3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$1105920$$ Trace bound: $$28$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3192))$$.

Total New Old
Modular forms 281664 111840 169824
Cusp forms 271297 110480 160817
Eisenstein series 10367 1360 9007

Trace form

 $$110480 q - 8 q^{2} - 72 q^{3} - 136 q^{4} - 8 q^{5} - 52 q^{6} - 164 q^{7} + 16 q^{8} - 144 q^{9} + O(q^{10})$$ $$110480 q - 8 q^{2} - 72 q^{3} - 136 q^{4} - 8 q^{5} - 52 q^{6} - 164 q^{7} + 16 q^{8} - 144 q^{9} - 104 q^{10} - 8 q^{11} - 28 q^{12} - 32 q^{13} + 8 q^{14} - 156 q^{15} - 120 q^{16} - 32 q^{17} - 84 q^{18} - 132 q^{19} + 40 q^{20} - 224 q^{22} + 72 q^{23} - 36 q^{24} - 204 q^{25} + 88 q^{26} - 18 q^{27} + 36 q^{28} - 48 q^{29} + 20 q^{30} - 48 q^{31} + 152 q^{32} - 152 q^{33} + 104 q^{34} - 116 q^{36} - 24 q^{37} + 52 q^{38} - 180 q^{39} + 32 q^{40} - 80 q^{41} - 142 q^{42} - 472 q^{43} - 96 q^{44} - 32 q^{45} - 272 q^{46} - 24 q^{47} - 212 q^{48} - 288 q^{49} - 176 q^{50} + 6 q^{51} - 272 q^{52} + 64 q^{53} - 228 q^{54} - 8 q^{55} - 184 q^{56} - 296 q^{57} - 432 q^{58} + 160 q^{59} - 192 q^{60} + 64 q^{61} + 128 q^{62} + 56 q^{63} + 32 q^{64} + 296 q^{65} + 68 q^{66} + 456 q^{67} + 384 q^{68} - 16 q^{69} + 164 q^{70} + 344 q^{71} - 24 q^{72} - 4 q^{73} + 640 q^{74} + 176 q^{75} + 540 q^{76} + 36 q^{77} + 68 q^{78} + 336 q^{79} + 576 q^{80} - 224 q^{81} + 816 q^{82} + 104 q^{83} - 94 q^{84} - 160 q^{85} + 472 q^{86} - 48 q^{87} + 520 q^{88} + 64 q^{89} - 232 q^{90} - 228 q^{91} + 336 q^{92} - 128 q^{93} - 24 q^{94} - 136 q^{95} - 324 q^{96} - 160 q^{97} - 128 q^{98} - 294 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3192))$$

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
3192.2.a $$\chi_{3192}(1, \cdot)$$ 3192.2.a.a 1 1
3192.2.a.b 1
3192.2.a.c 1
3192.2.a.d 1
3192.2.a.e 1
3192.2.a.f 1
3192.2.a.g 1
3192.2.a.h 1
3192.2.a.i 1
3192.2.a.j 1
3192.2.a.k 1
3192.2.a.l 1
3192.2.a.m 1
3192.2.a.n 1
3192.2.a.o 1
3192.2.a.p 1
3192.2.a.q 2
3192.2.a.r 2
3192.2.a.s 2
3192.2.a.t 2
3192.2.a.u 3
3192.2.a.v 3
3192.2.a.w 4
3192.2.a.x 4
3192.2.a.y 4
3192.2.a.z 4
3192.2.a.ba 5
3192.2.a.bb 5
3192.2.b $$\chi_{3192}(113, \cdot)$$ n/a 120 1
3192.2.c $$\chi_{3192}(3079, \cdot)$$ None 0 1
3192.2.d $$\chi_{3192}(1595, \cdot)$$ n/a 632 1
3192.2.e $$\chi_{3192}(1597, \cdot)$$ n/a 216 1
3192.2.n $$\chi_{3192}(2927, \cdot)$$ None 0 1
3192.2.o $$\chi_{3192}(265, \cdot)$$ 3192.2.o.a 40 1
3192.2.o.b 40
3192.2.p $$\chi_{3192}(2813, \cdot)$$ n/a 576 1
3192.2.q $$\chi_{3192}(379, \cdot)$$ n/a 240 1
3192.2.r $$\chi_{3192}(1331, \cdot)$$ n/a 432 1
3192.2.s $$\chi_{3192}(1861, \cdot)$$ n/a 320 1
3192.2.t $$\chi_{3192}(1217, \cdot)$$ n/a 144 1
3192.2.u $$\chi_{3192}(1975, \cdot)$$ None 0 1
3192.2.bd $$\chi_{3192}(1709, \cdot)$$ n/a 480 1
3192.2.be $$\chi_{3192}(1483, \cdot)$$ n/a 288 1
3192.2.bf $$\chi_{3192}(3191, \cdot)$$ None 0 1
3192.2.bg $$\chi_{3192}(961, \cdot)$$ n/a 160 2
3192.2.bh $$\chi_{3192}(457, \cdot)$$ n/a 144 2
3192.2.bi $$\chi_{3192}(505, \cdot)$$ n/a 120 2
3192.2.bj $$\chi_{3192}(121, \cdot)$$ n/a 160 2
3192.2.bk $$\chi_{3192}(1171, \cdot)$$ n/a 640 2
3192.2.bl $$\chi_{3192}(1949, \cdot)$$ n/a 1264 2
3192.2.bm $$\chi_{3192}(145, \cdot)$$ n/a 160 2
3192.2.bn $$\chi_{3192}(1607, \cdot)$$ None 0 2
3192.2.bw $$\chi_{3192}(277, \cdot)$$ n/a 640 2
3192.2.bx $$\chi_{3192}(1475, \cdot)$$ n/a 1264 2
3192.2.by $$\chi_{3192}(2215, \cdot)$$ None 0 2
3192.2.bz $$\chi_{3192}(905, \cdot)$$ n/a 320 2
3192.2.ce $$\chi_{3192}(881, \cdot)$$ n/a 320 2
3192.2.cf $$\chi_{3192}(1471, \cdot)$$ None 0 2
3192.2.cg $$\chi_{3192}(995, \cdot)$$ n/a 960 2
3192.2.ch $$\chi_{3192}(1357, \cdot)$$ n/a 640 2
3192.2.cm $$\chi_{3192}(1531, \cdot)$$ n/a 640 2
3192.2.cn $$\chi_{3192}(221, \cdot)$$ n/a 1264 2
3192.2.co $$\chi_{3192}(2159, \cdot)$$ None 0 2
3192.2.ct $$\chi_{3192}(1823, \cdot)$$ None 0 2
3192.2.cu $$\chi_{3192}(115, \cdot)$$ n/a 576 2
3192.2.cv $$\chi_{3192}(2165, \cdot)$$ n/a 1264 2
3192.2.cw $$\chi_{3192}(151, \cdot)$$ None 0 2
3192.2.cx $$\chi_{3192}(761, \cdot)$$ n/a 288 2
3192.2.cy $$\chi_{3192}(493, \cdot)$$ n/a 640 2
3192.2.cz $$\chi_{3192}(1787, \cdot)$$ n/a 1152 2
3192.2.de $$\chi_{3192}(829, \cdot)$$ n/a 640 2
3192.2.df $$\chi_{3192}(2291, \cdot)$$ n/a 1264 2
3192.2.dg $$\chi_{3192}(487, \cdot)$$ None 0 2
3192.2.dh $$\chi_{3192}(1265, \cdot)$$ n/a 320 2
3192.2.dm $$\chi_{3192}(335, \cdot)$$ None 0 2
3192.2.dn $$\chi_{3192}(1205, \cdot)$$ n/a 960 2
3192.2.do $$\chi_{3192}(1147, \cdot)$$ n/a 640 2
3192.2.dx $$\chi_{3192}(1091, \cdot)$$ n/a 1264 2
3192.2.dy $$\chi_{3192}(1261, \cdot)$$ n/a 480 2
3192.2.dz $$\chi_{3192}(449, \cdot)$$ n/a 240 2
3192.2.ea $$\chi_{3192}(391, \cdot)$$ None 0 2
3192.2.ef $$\chi_{3192}(2425, \cdot)$$ n/a 160 2
3192.2.eg $$\chi_{3192}(695, \cdot)$$ None 0 2
3192.2.eh $$\chi_{3192}(331, \cdot)$$ n/a 640 2
3192.2.ei $$\chi_{3192}(1109, \cdot)$$ n/a 1264 2
3192.2.en $$\chi_{3192}(835, \cdot)$$ n/a 640 2
3192.2.eo $$\chi_{3192}(1445, \cdot)$$ n/a 1152 2
3192.2.ep $$\chi_{3192}(2089, \cdot)$$ n/a 160 2
3192.2.eq $$\chi_{3192}(191, \cdot)$$ None 0 2
3192.2.er $$\chi_{3192}(2053, \cdot)$$ n/a 576 2
3192.2.es $$\chi_{3192}(227, \cdot)$$ n/a 1264 2
3192.2.et $$\chi_{3192}(1711, \cdot)$$ None 0 2
3192.2.eu $$\chi_{3192}(569, \cdot)$$ n/a 320 2
3192.2.ez $$\chi_{3192}(1375, \cdot)$$ None 0 2
3192.2.fa $$\chi_{3192}(65, \cdot)$$ n/a 320 2
3192.2.fb $$\chi_{3192}(2557, \cdot)$$ n/a 640 2
3192.2.fc $$\chi_{3192}(563, \cdot)$$ n/a 1264 2
3192.2.fh $$\chi_{3192}(125, \cdot)$$ n/a 1264 2
3192.2.fi $$\chi_{3192}(715, \cdot)$$ n/a 480 2
3192.2.fj $$\chi_{3192}(239, \cdot)$$ None 0 2
3192.2.fk $$\chi_{3192}(601, \cdot)$$ n/a 160 2
3192.2.fp $$\chi_{3192}(1319, \cdot)$$ None 0 2
3192.2.fq $$\chi_{3192}(619, \cdot)$$ n/a 640 2
3192.2.fr $$\chi_{3192}(2501, \cdot)$$ n/a 1264 2
3192.2.ga $$\chi_{3192}(2767, \cdot)$$ None 0 2
3192.2.gb $$\chi_{3192}(353, \cdot)$$ n/a 320 2
3192.2.gc $$\chi_{3192}(1741, \cdot)$$ n/a 640 2
3192.2.gd $$\chi_{3192}(11, \cdot)$$ n/a 1264 2
3192.2.ge $$\chi_{3192}(169, \cdot)$$ n/a 360 6
3192.2.gf $$\chi_{3192}(289, \cdot)$$ n/a 480 6
3192.2.gg $$\chi_{3192}(25, \cdot)$$ n/a 480 6
3192.2.gh $$\chi_{3192}(199, \cdot)$$ None 0 6
3192.2.gj $$\chi_{3192}(565, \cdot)$$ n/a 1920 6
3192.2.gm $$\chi_{3192}(1213, \cdot)$$ n/a 1920 6
3192.2.go $$\chi_{3192}(79, \cdot)$$ None 0 6
3192.2.gp $$\chi_{3192}(299, \cdot)$$ n/a 3792 6
3192.2.gr $$\chi_{3192}(929, \cdot)$$ n/a 960 6
3192.2.gu $$\chi_{3192}(401, \cdot)$$ n/a 960 6
3192.2.gw $$\chi_{3192}(947, \cdot)$$ n/a 3792 6
3192.2.gx $$\chi_{3192}(23, \cdot)$$ None 0 6
3192.2.gz $$\chi_{3192}(317, \cdot)$$ n/a 3792 6
3192.2.hc $$\chi_{3192}(605, \cdot)$$ n/a 3792 6
3192.2.he $$\chi_{3192}(887, \cdot)$$ None 0 6
3192.2.hg $$\chi_{3192}(139, \cdot)$$ n/a 1920 6
3192.2.hi $$\chi_{3192}(97, \cdot)$$ n/a 480 6
3192.2.hk $$\chi_{3192}(211, \cdot)$$ n/a 1440 6
3192.2.hn $$\chi_{3192}(167, \cdot)$$ None 0 6
3192.2.hp $$\chi_{3192}(461, \cdot)$$ n/a 3792 6
3192.2.hq $$\chi_{3192}(29, \cdot)$$ n/a 2880 6
3192.2.hs $$\chi_{3192}(575, \cdot)$$ None 0 6
3192.2.hu $$\chi_{3192}(907, \cdot)$$ n/a 1920 6
3192.2.hy $$\chi_{3192}(1153, \cdot)$$ n/a 480 6
3192.2.ia $$\chi_{3192}(283, \cdot)$$ n/a 1920 6
3192.2.ib $$\chi_{3192}(17, \cdot)$$ n/a 960 6
3192.2.id $$\chi_{3192}(59, \cdot)$$ n/a 3792 6
3192.2.ig $$\chi_{3192}(275, \cdot)$$ n/a 3792 6
3192.2.ii $$\chi_{3192}(641, \cdot)$$ n/a 960 6
3192.2.ik $$\chi_{3192}(85, \cdot)$$ n/a 1440 6
3192.2.im $$\chi_{3192}(127, \cdot)$$ None 0 6
3192.2.in $$\chi_{3192}(55, \cdot)$$ None 0 6
3192.2.ip $$\chi_{3192}(13, \cdot)$$ n/a 1920 6
3192.2.is $$\chi_{3192}(281, \cdot)$$ n/a 720 6
3192.2.iu $$\chi_{3192}(491, \cdot)$$ n/a 2880 6
3192.2.iv $$\chi_{3192}(755, \cdot)$$ n/a 3792 6
3192.2.ix $$\chi_{3192}(377, \cdot)$$ n/a 960 6
3192.2.iz $$\chi_{3192}(325, \cdot)$$ n/a 1920 6
3192.2.jb $$\chi_{3192}(871, \cdot)$$ None 0 6
3192.2.je $$\chi_{3192}(583, \cdot)$$ None 0 6
3192.2.jg $$\chi_{3192}(541, \cdot)$$ n/a 1920 6
3192.2.ji $$\chi_{3192}(67, \cdot)$$ n/a 1920 6
3192.2.jl $$\chi_{3192}(187, \cdot)$$ n/a 1920 6
3192.2.jn $$\chi_{3192}(241, \cdot)$$ n/a 480 6
3192.2.jo $$\chi_{3192}(53, \cdot)$$ n/a 3792 6
3192.2.jq $$\chi_{3192}(359, \cdot)$$ None 0 6
3192.2.jt $$\chi_{3192}(143, \cdot)$$ None 0 6
3192.2.jv $$\chi_{3192}(5, \cdot)$$ n/a 3792 6

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3192))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3192)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(399))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(798))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1064))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1596))$$$$^{\oplus 2}$$