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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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

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