# Properties

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

## 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

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

## 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 the 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

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