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Properties

Label 3696.2
Level 3696
Weight 2
Dimension 145748
Nonzero newspaces 64
Sturm bound 1474560
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(1474560\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3696))\).

Total New Old
Modular forms 375360 147364 227996
Cusp forms 361921 145748 216173
Eisenstein series 13439 1616 11823

Trace form

\( 145748 q - 46 q^{3} - 144 q^{4} - 8 q^{5} - 88 q^{6} - 130 q^{7} - 48 q^{8} - 34 q^{9} + O(q^{10}) \) \( 145748 q - 46 q^{3} - 144 q^{4} - 8 q^{5} - 88 q^{6} - 130 q^{7} - 48 q^{8} - 34 q^{9} - 144 q^{10} - 24 q^{11} - 136 q^{12} - 192 q^{13} + 24 q^{14} - 154 q^{15} - 48 q^{16} + 8 q^{17} - 24 q^{18} - 172 q^{19} + 64 q^{20} - 116 q^{21} - 320 q^{22} - 40 q^{23} + 56 q^{24} - 88 q^{25} + 80 q^{26} - 4 q^{27} - 152 q^{28} - 88 q^{29} + 24 q^{30} - 116 q^{31} - 233 q^{33} - 304 q^{34} - 84 q^{35} - 88 q^{36} - 404 q^{37} - 32 q^{38} - 84 q^{39} - 208 q^{40} - 184 q^{41} - 20 q^{42} - 304 q^{43} + 16 q^{44} - 250 q^{45} - 64 q^{46} - 48 q^{47} - 72 q^{48} - 362 q^{49} + 192 q^{50} + 34 q^{51} + 192 q^{52} + 168 q^{53} + 88 q^{54} - 80 q^{55} + 336 q^{56} + 82 q^{57} + 288 q^{58} + 208 q^{59} + 312 q^{60} + 268 q^{61} + 384 q^{62} + 19 q^{63} + 288 q^{64} + 144 q^{65} + 156 q^{66} - 68 q^{67} + 368 q^{68} + 150 q^{69} + 464 q^{70} + 32 q^{71} + 360 q^{72} + 412 q^{73} + 608 q^{74} + 100 q^{75} + 784 q^{76} + 176 q^{77} + 320 q^{78} + 52 q^{79} + 912 q^{80} - 2 q^{81} + 784 q^{82} + 56 q^{83} + 148 q^{84} + 308 q^{85} + 576 q^{86} + 38 q^{87} + 1080 q^{88} + 296 q^{89} + 8 q^{90} + 298 q^{91} + 528 q^{92} + 306 q^{93} + 400 q^{94} + 336 q^{95} - 120 q^{96} + 80 q^{97} + 24 q^{98} - 124 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3696))\)

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
3696.2.a \(\chi_{3696}(1, \cdot)\) 3696.2.a.a 1 1
3696.2.a.b 1
3696.2.a.c 1
3696.2.a.d 1
3696.2.a.e 1
3696.2.a.f 1
3696.2.a.g 1
3696.2.a.h 1
3696.2.a.i 1
3696.2.a.j 1
3696.2.a.k 1
3696.2.a.l 1
3696.2.a.m 1
3696.2.a.n 1
3696.2.a.o 1
3696.2.a.p 1
3696.2.a.q 1
3696.2.a.r 1
3696.2.a.s 1
3696.2.a.t 1
3696.2.a.u 1
3696.2.a.v 1
3696.2.a.w 1
3696.2.a.x 1
3696.2.a.y 1
3696.2.a.z 1
3696.2.a.ba 1
3696.2.a.bb 1
3696.2.a.bc 2
3696.2.a.bd 2
3696.2.a.be 2
3696.2.a.bf 2
3696.2.a.bg 2
3696.2.a.bh 2
3696.2.a.bi 2
3696.2.a.bj 2
3696.2.a.bk 2
3696.2.a.bl 2
3696.2.a.bm 3
3696.2.a.bn 3
3696.2.a.bo 3
3696.2.a.bp 3
3696.2.d \(\chi_{3696}(2575, \cdot)\) 3696.2.d.a 4 1
3696.2.d.b 4
3696.2.d.c 8
3696.2.d.d 8
3696.2.d.e 28
3696.2.d.f 28
3696.2.e \(\chi_{3696}(1847, \cdot)\) None 0 1
3696.2.f \(\chi_{3696}(1121, \cdot)\) n/a 144 1
3696.2.g \(\chi_{3696}(1849, \cdot)\) None 0 1
3696.2.j \(\chi_{3696}(967, \cdot)\) None 0 1
3696.2.k \(\chi_{3696}(2927, \cdot)\) n/a 120 1
3696.2.p \(\chi_{3696}(2729, \cdot)\) None 0 1
3696.2.q \(\chi_{3696}(769, \cdot)\) 3696.2.q.a 4 1
3696.2.q.b 8
3696.2.q.c 8
3696.2.q.d 12
3696.2.q.e 16
3696.2.q.f 24
3696.2.q.g 24
3696.2.t \(\chi_{3696}(2815, \cdot)\) 3696.2.t.a 12 1
3696.2.t.b 12
3696.2.t.c 24
3696.2.t.d 24
3696.2.u \(\chi_{3696}(1079, \cdot)\) None 0 1
3696.2.v \(\chi_{3696}(881, \cdot)\) n/a 160 1
3696.2.w \(\chi_{3696}(2617, \cdot)\) None 0 1
3696.2.z \(\chi_{3696}(727, \cdot)\) None 0 1
3696.2.ba \(\chi_{3696}(3695, \cdot)\) n/a 192 1
3696.2.bf \(\chi_{3696}(2969, \cdot)\) None 0 1
3696.2.bg \(\chi_{3696}(529, \cdot)\) n/a 160 2
3696.2.bi \(\chi_{3696}(155, \cdot)\) n/a 960 2
3696.2.bj \(\chi_{3696}(923, \cdot)\) n/a 1520 2
3696.2.bl \(\chi_{3696}(43, \cdot)\) n/a 576 2
3696.2.bo \(\chi_{3696}(1651, \cdot)\) n/a 640 2
3696.2.bp \(\chi_{3696}(1693, \cdot)\) n/a 768 2
3696.2.bs \(\chi_{3696}(925, \cdot)\) n/a 480 2
3696.2.bu \(\chi_{3696}(1805, \cdot)\) n/a 1280 2
3696.2.bv \(\chi_{3696}(197, \cdot)\) n/a 1152 2
3696.2.bx \(\chi_{3696}(1345, \cdot)\) n/a 288 4
3696.2.ca \(\chi_{3696}(2089, \cdot)\) None 0 2
3696.2.cb \(\chi_{3696}(353, \cdot)\) n/a 320 2
3696.2.cc \(\chi_{3696}(23, \cdot)\) None 0 2
3696.2.cd \(\chi_{3696}(1759, \cdot)\) n/a 192 2
3696.2.cg \(\chi_{3696}(1913, \cdot)\) None 0 2
3696.2.cl \(\chi_{3696}(1055, \cdot)\) n/a 384 2
3696.2.cm \(\chi_{3696}(199, \cdot)\) None 0 2
3696.2.cp \(\chi_{3696}(793, \cdot)\) None 0 2
3696.2.cq \(\chi_{3696}(65, \cdot)\) n/a 376 2
3696.2.cr \(\chi_{3696}(1319, \cdot)\) None 0 2
3696.2.cs \(\chi_{3696}(2047, \cdot)\) n/a 160 2
3696.2.cv \(\chi_{3696}(241, \cdot)\) n/a 192 2
3696.2.cw \(\chi_{3696}(89, \cdot)\) None 0 2
3696.2.db \(\chi_{3696}(1871, \cdot)\) n/a 320 2
3696.2.dc \(\chi_{3696}(1495, \cdot)\) None 0 2
3696.2.dd \(\chi_{3696}(281, \cdot)\) None 0 4
3696.2.di \(\chi_{3696}(2071, \cdot)\) None 0 4
3696.2.dj \(\chi_{3696}(1007, \cdot)\) n/a 768 4
3696.2.dm \(\chi_{3696}(2225, \cdot)\) n/a 752 4
3696.2.dn \(\chi_{3696}(601, \cdot)\) None 0 4
3696.2.do \(\chi_{3696}(127, \cdot)\) n/a 288 4
3696.2.dp \(\chi_{3696}(71, \cdot)\) None 0 4
3696.2.ds \(\chi_{3696}(377, \cdot)\) None 0 4
3696.2.dt \(\chi_{3696}(1777, \cdot)\) n/a 384 4
3696.2.dy \(\chi_{3696}(1975, \cdot)\) None 0 4
3696.2.dz \(\chi_{3696}(575, \cdot)\) n/a 576 4
3696.2.ec \(\chi_{3696}(2129, \cdot)\) n/a 576 4
3696.2.ed \(\chi_{3696}(169, \cdot)\) None 0 4
3696.2.ee \(\chi_{3696}(223, \cdot)\) n/a 384 4
3696.2.ef \(\chi_{3696}(167, \cdot)\) None 0 4
3696.2.ej \(\chi_{3696}(725, \cdot)\) n/a 3040 4
3696.2.ek \(\chi_{3696}(1013, \cdot)\) n/a 2560 4
3696.2.em \(\chi_{3696}(1453, \cdot)\) n/a 1280 4
3696.2.ep \(\chi_{3696}(901, \cdot)\) n/a 1536 4
3696.2.eq \(\chi_{3696}(859, \cdot)\) n/a 1280 4
3696.2.et \(\chi_{3696}(571, \cdot)\) n/a 1536 4
3696.2.ev \(\chi_{3696}(131, \cdot)\) n/a 3040 4
3696.2.ew \(\chi_{3696}(683, \cdot)\) n/a 2560 4
3696.2.ey \(\chi_{3696}(289, \cdot)\) n/a 768 8
3696.2.ez \(\chi_{3696}(421, \cdot)\) n/a 2304 8
3696.2.fc \(\chi_{3696}(13, \cdot)\) n/a 3072 8
3696.2.fe \(\chi_{3696}(29, \cdot)\) n/a 4608 8
3696.2.ff \(\chi_{3696}(125, \cdot)\) n/a 6080 8
3696.2.fi \(\chi_{3696}(83, \cdot)\) n/a 6080 8
3696.2.fj \(\chi_{3696}(323, \cdot)\) n/a 4608 8
3696.2.fl \(\chi_{3696}(643, \cdot)\) n/a 3072 8
3696.2.fo \(\chi_{3696}(211, \cdot)\) n/a 2304 8
3696.2.fp \(\chi_{3696}(191, \cdot)\) n/a 1536 8
3696.2.fq \(\chi_{3696}(151, \cdot)\) None 0 8
3696.2.fv \(\chi_{3696}(145, \cdot)\) n/a 768 8
3696.2.fw \(\chi_{3696}(185, \cdot)\) None 0 8
3696.2.fz \(\chi_{3696}(215, \cdot)\) None 0 8
3696.2.ga \(\chi_{3696}(31, \cdot)\) n/a 768 8
3696.2.gb \(\chi_{3696}(25, \cdot)\) None 0 8
3696.2.gc \(\chi_{3696}(305, \cdot)\) n/a 1504 8
3696.2.gf \(\chi_{3696}(479, \cdot)\) n/a 1536 8
3696.2.gg \(\chi_{3696}(103, \cdot)\) None 0 8
3696.2.gl \(\chi_{3696}(233, \cdot)\) None 0 8
3696.2.go \(\chi_{3696}(599, \cdot)\) None 0 8
3696.2.gp \(\chi_{3696}(79, \cdot)\) n/a 768 8
3696.2.gq \(\chi_{3696}(73, \cdot)\) None 0 8
3696.2.gr \(\chi_{3696}(257, \cdot)\) n/a 1504 8
3696.2.gu \(\chi_{3696}(403, \cdot)\) n/a 6144 16
3696.2.gx \(\chi_{3696}(115, \cdot)\) n/a 6144 16
3696.2.gz \(\chi_{3696}(179, \cdot)\) n/a 12160 16
3696.2.ha \(\chi_{3696}(227, \cdot)\) n/a 12160 16
3696.2.hd \(\chi_{3696}(5, \cdot)\) n/a 12160 16
3696.2.he \(\chi_{3696}(149, \cdot)\) n/a 12160 16
3696.2.hg \(\chi_{3696}(61, \cdot)\) n/a 6144 16
3696.2.hj \(\chi_{3696}(37, \cdot)\) n/a 6144 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3696))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3696)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(924))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1848))\)\(^{\oplus 2}\)