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Properties

Label 3432.2
Level 3432
Weight 2
Dimension 131428
Nonzero newspaces 72
Sturm bound 1290240
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(1290240\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3432))\).

Total New Old
Modular forms 328320 133012 195308
Cusp forms 316801 131428 185373
Eisenstein series 11519 1584 9935

Trace form

\( 131428 q - 8 q^{2} - 88 q^{3} - 168 q^{4} - 8 q^{5} - 68 q^{6} - 168 q^{7} + 16 q^{8} - 164 q^{9} + O(q^{10}) \) \( 131428 q - 8 q^{2} - 88 q^{3} - 168 q^{4} - 8 q^{5} - 68 q^{6} - 168 q^{7} + 16 q^{8} - 164 q^{9} - 136 q^{10} + 8 q^{11} - 144 q^{12} - 4 q^{13} + 16 q^{14} - 72 q^{15} - 152 q^{16} - 60 q^{17} - 100 q^{18} - 260 q^{19} - 32 q^{20} - 88 q^{21} - 192 q^{22} - 88 q^{23} - 124 q^{24} - 480 q^{25} - 16 q^{26} - 208 q^{27} - 152 q^{28} - 76 q^{29} - 32 q^{30} - 192 q^{31} + 72 q^{32} - 162 q^{33} - 112 q^{34} + 72 q^{35} + 100 q^{36} + 12 q^{37} + 232 q^{38} - 14 q^{39} + 160 q^{40} + 148 q^{41} + 304 q^{42} + 136 q^{43} + 400 q^{44} + 88 q^{45} + 576 q^{46} + 168 q^{47} + 304 q^{48} - 132 q^{49} + 704 q^{50} + 150 q^{51} + 392 q^{52} + 136 q^{53} + 108 q^{54} + 72 q^{55} + 560 q^{56} + 14 q^{57} + 224 q^{58} + 160 q^{59} + 264 q^{60} + 172 q^{61} + 224 q^{62} + 92 q^{63} + 72 q^{64} + 76 q^{65} - 132 q^{66} - 208 q^{67} + 184 q^{69} - 224 q^{70} + 208 q^{71} - 68 q^{72} - 176 q^{73} - 136 q^{74} + 390 q^{75} - 568 q^{76} + 120 q^{77} - 300 q^{78} + 104 q^{79} - 440 q^{80} - 60 q^{81} - 696 q^{82} + 384 q^{83} - 516 q^{84} + 260 q^{85} - 544 q^{86} + 312 q^{87} - 904 q^{88} + 160 q^{89} - 444 q^{90} + 432 q^{91} - 608 q^{92} + 244 q^{93} - 920 q^{94} + 768 q^{95} - 672 q^{96} - 188 q^{97} - 848 q^{98} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3432))\)

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
3432.2.a \(\chi_{3432}(1, \cdot)\) 3432.2.a.a 1 1
3432.2.a.b 1
3432.2.a.c 1
3432.2.a.d 1
3432.2.a.e 1
3432.2.a.f 1
3432.2.a.g 1
3432.2.a.h 1
3432.2.a.i 1
3432.2.a.j 2
3432.2.a.k 2
3432.2.a.l 2
3432.2.a.m 2
3432.2.a.n 3
3432.2.a.o 3
3432.2.a.p 3
3432.2.a.q 4
3432.2.a.r 4
3432.2.a.s 4
3432.2.a.t 4
3432.2.a.u 4
3432.2.a.v 4
3432.2.a.w 5
3432.2.a.x 5
3432.2.b \(\chi_{3432}(2287, \cdot)\) None 0 1
3432.2.c \(\chi_{3432}(287, \cdot)\) None 0 1
3432.2.f \(\chi_{3432}(2705, \cdot)\) n/a 144 1
3432.2.g \(\chi_{3432}(1585, \cdot)\) 3432.2.g.a 2 1
3432.2.g.b 2
3432.2.g.c 14
3432.2.g.d 14
3432.2.g.e 20
3432.2.g.f 20
3432.2.j \(\chi_{3432}(2419, \cdot)\) n/a 288 1
3432.2.k \(\chi_{3432}(155, \cdot)\) n/a 560 1
3432.2.n \(\chi_{3432}(2573, \cdot)\) n/a 664 1
3432.2.o \(\chi_{3432}(1717, \cdot)\) n/a 240 1
3432.2.t \(\chi_{3432}(571, \cdot)\) n/a 336 1
3432.2.u \(\chi_{3432}(2003, \cdot)\) n/a 480 1
3432.2.x \(\chi_{3432}(989, \cdot)\) n/a 576 1
3432.2.y \(\chi_{3432}(3301, \cdot)\) n/a 280 1
3432.2.bb \(\chi_{3432}(703, \cdot)\) None 0 1
3432.2.bc \(\chi_{3432}(1871, \cdot)\) None 0 1
3432.2.bf \(\chi_{3432}(857, \cdot)\) n/a 168 1
3432.2.bg \(\chi_{3432}(529, \cdot)\) n/a 136 2
3432.2.bi \(\chi_{3432}(395, \cdot)\) n/a 1328 2
3432.2.bj \(\chi_{3432}(2111, \cdot)\) None 0 2
3432.2.bm \(\chi_{3432}(1123, \cdot)\) n/a 560 2
3432.2.bn \(\chi_{3432}(463, \cdot)\) None 0 2
3432.2.bp \(\chi_{3432}(1825, \cdot)\) n/a 168 2
3432.2.bs \(\chi_{3432}(109, \cdot)\) n/a 672 2
3432.2.bt \(\chi_{3432}(1409, \cdot)\) n/a 280 2
3432.2.bw \(\chi_{3432}(749, \cdot)\) n/a 1120 2
3432.2.bx \(\chi_{3432}(313, \cdot)\) n/a 288 4
3432.2.ca \(\chi_{3432}(133, \cdot)\) n/a 560 2
3432.2.cb \(\chi_{3432}(725, \cdot)\) n/a 1328 2
3432.2.ce \(\chi_{3432}(1739, \cdot)\) n/a 1120 2
3432.2.cf \(\chi_{3432}(835, \cdot)\) n/a 672 2
3432.2.ci \(\chi_{3432}(1057, \cdot)\) n/a 144 2
3432.2.cj \(\chi_{3432}(1121, \cdot)\) n/a 336 2
3432.2.cm \(\chi_{3432}(815, \cdot)\) None 0 2
3432.2.cn \(\chi_{3432}(439, \cdot)\) None 0 2
3432.2.co \(\chi_{3432}(329, \cdot)\) n/a 336 2
3432.2.cr \(\chi_{3432}(23, \cdot)\) None 0 2
3432.2.cs \(\chi_{3432}(1231, \cdot)\) None 0 2
3432.2.cv \(\chi_{3432}(1453, \cdot)\) n/a 560 2
3432.2.cw \(\chi_{3432}(1517, \cdot)\) n/a 1328 2
3432.2.cz \(\chi_{3432}(419, \cdot)\) n/a 1120 2
3432.2.da \(\chi_{3432}(43, \cdot)\) n/a 672 2
3432.2.dd \(\chi_{3432}(233, \cdot)\) n/a 672 4
3432.2.dg \(\chi_{3432}(79, \cdot)\) None 0 4
3432.2.dh \(\chi_{3432}(311, \cdot)\) None 0 4
3432.2.dk \(\chi_{3432}(365, \cdot)\) n/a 2304 4
3432.2.dl \(\chi_{3432}(181, \cdot)\) n/a 1344 4
3432.2.do \(\chi_{3432}(259, \cdot)\) n/a 1344 4
3432.2.dp \(\chi_{3432}(443, \cdot)\) n/a 2304 4
3432.2.du \(\chi_{3432}(701, \cdot)\) n/a 2656 4
3432.2.dv \(\chi_{3432}(157, \cdot)\) n/a 1152 4
3432.2.dy \(\chi_{3432}(547, \cdot)\) n/a 1152 4
3432.2.dz \(\chi_{3432}(467, \cdot)\) n/a 2656 4
3432.2.ec \(\chi_{3432}(833, \cdot)\) n/a 576 4
3432.2.ed \(\chi_{3432}(25, \cdot)\) n/a 336 4
3432.2.eg \(\chi_{3432}(415, \cdot)\) None 0 4
3432.2.eh \(\chi_{3432}(599, \cdot)\) None 0 4
3432.2.ei \(\chi_{3432}(1541, \cdot)\) n/a 2240 4
3432.2.el \(\chi_{3432}(89, \cdot)\) n/a 560 4
3432.2.em \(\chi_{3432}(1957, \cdot)\) n/a 1344 4
3432.2.ep \(\chi_{3432}(241, \cdot)\) n/a 336 4
3432.2.er \(\chi_{3432}(1255, \cdot)\) None 0 4
3432.2.es \(\chi_{3432}(67, \cdot)\) n/a 1120 4
3432.2.ev \(\chi_{3432}(527, \cdot)\) None 0 4
3432.2.ew \(\chi_{3432}(2243, \cdot)\) n/a 2656 4
3432.2.ey \(\chi_{3432}(289, \cdot)\) n/a 672 8
3432.2.ez \(\chi_{3432}(541, \cdot)\) n/a 2688 8
3432.2.fc \(\chi_{3432}(73, \cdot)\) n/a 672 8
3432.2.fd \(\chi_{3432}(5, \cdot)\) n/a 5312 8
3432.2.fg \(\chi_{3432}(785, \cdot)\) n/a 1344 8
3432.2.fi \(\chi_{3432}(239, \cdot)\) None 0 8
3432.2.fj \(\chi_{3432}(83, \cdot)\) n/a 5312 8
3432.2.fm \(\chi_{3432}(31, \cdot)\) None 0 8
3432.2.fn \(\chi_{3432}(499, \cdot)\) n/a 2688 8
3432.2.fr \(\chi_{3432}(731, \cdot)\) n/a 5312 8
3432.2.fs \(\chi_{3432}(283, \cdot)\) n/a 2688 8
3432.2.fv \(\chi_{3432}(829, \cdot)\) n/a 2688 8
3432.2.fw \(\chi_{3432}(29, \cdot)\) n/a 5312 8
3432.2.fz \(\chi_{3432}(335, \cdot)\) None 0 8
3432.2.ga \(\chi_{3432}(607, \cdot)\) None 0 8
3432.2.gd \(\chi_{3432}(17, \cdot)\) n/a 1344 8
3432.2.ge \(\chi_{3432}(191, \cdot)\) None 0 8
3432.2.gf \(\chi_{3432}(127, \cdot)\) None 0 8
3432.2.gi \(\chi_{3432}(49, \cdot)\) n/a 672 8
3432.2.gj \(\chi_{3432}(425, \cdot)\) n/a 1344 8
3432.2.gm \(\chi_{3432}(179, \cdot)\) n/a 5312 8
3432.2.gn \(\chi_{3432}(139, \cdot)\) n/a 2688 8
3432.2.gq \(\chi_{3432}(445, \cdot)\) n/a 2688 8
3432.2.gr \(\chi_{3432}(101, \cdot)\) n/a 5312 8
3432.2.gv \(\chi_{3432}(115, \cdot)\) n/a 5376 16
3432.2.gw \(\chi_{3432}(223, \cdot)\) None 0 16
3432.2.gz \(\chi_{3432}(227, \cdot)\) n/a 10624 16
3432.2.ha \(\chi_{3432}(167, \cdot)\) None 0 16
3432.2.hc \(\chi_{3432}(137, \cdot)\) n/a 2688 16
3432.2.hf \(\chi_{3432}(245, \cdot)\) n/a 10624 16
3432.2.hg \(\chi_{3432}(145, \cdot)\) n/a 1344 16
3432.2.hj \(\chi_{3432}(85, \cdot)\) n/a 5376 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3432))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3432)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1716))\)\(^{\oplus 2}\)