# Properties

 Label 3920.2 Level 3920 Weight 2 Dimension 222134 Nonzero newspaces 56 Sturm bound 1806336 Trace bound 14

## Defining parameters

 Level: $$N$$ = $$3920 = 2^{4} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$1806336$$ Trace bound: $$14$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3920))$$.

Total New Old
Modular forms 458304 224752 233552
Cusp forms 444865 222134 222731
Eisenstein series 13439 2618 10821

## Trace form

 $$222134 q - 124 q^{2} - 92 q^{3} - 128 q^{4} - 233 q^{5} - 384 q^{6} - 108 q^{7} - 232 q^{8} - 34 q^{9} + O(q^{10})$$ $$222134 q - 124 q^{2} - 92 q^{3} - 128 q^{4} - 233 q^{5} - 384 q^{6} - 108 q^{7} - 232 q^{8} - 34 q^{9} - 188 q^{10} - 286 q^{11} - 120 q^{12} - 172 q^{13} - 144 q^{14} - 265 q^{15} - 360 q^{16} - 288 q^{17} - 132 q^{18} - 142 q^{19} - 192 q^{20} - 564 q^{21} - 224 q^{22} - 180 q^{23} - 128 q^{24} - 103 q^{25} - 384 q^{26} - 170 q^{27} - 144 q^{28} - 338 q^{29} - 152 q^{30} - 338 q^{31} - 104 q^{32} - 350 q^{33} - 72 q^{34} - 180 q^{35} - 592 q^{36} - 180 q^{37} - 48 q^{38} - 58 q^{39} - 100 q^{40} - 74 q^{41} - 148 q^{43} + 128 q^{44} - 129 q^{45} - 96 q^{46} - 56 q^{47} + 400 q^{48} - 228 q^{49} - 480 q^{50} - 186 q^{51} + 344 q^{52} + 36 q^{53} + 592 q^{54} - 77 q^{55} - 264 q^{56} + 290 q^{57} + 232 q^{58} - 22 q^{59} + 116 q^{60} - 258 q^{61} + 272 q^{62} - 48 q^{63} + 88 q^{64} - 389 q^{65} + 32 q^{66} + 8 q^{67} + 56 q^{68} - 30 q^{69} - 168 q^{70} - 562 q^{71} + 128 q^{72} - 148 q^{73} - 216 q^{74} - 137 q^{75} - 464 q^{76} - 276 q^{77} - 352 q^{78} - 170 q^{79} - 276 q^{80} - 1096 q^{81} - 192 q^{82} - 208 q^{83} - 144 q^{84} - 511 q^{85} - 440 q^{86} - 154 q^{87} - 232 q^{88} - 246 q^{89} - 448 q^{90} - 198 q^{91} - 264 q^{92} - 350 q^{93} - 440 q^{94} - 11 q^{95} - 888 q^{96} - 374 q^{97} - 312 q^{98} + 240 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3920))$$

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
3920.2.a $$\chi_{3920}(1, \cdot)$$ 3920.2.a.a 1 1
3920.2.a.b 1
3920.2.a.c 1
3920.2.a.d 1
3920.2.a.e 1
3920.2.a.f 1
3920.2.a.g 1
3920.2.a.h 1
3920.2.a.i 1
3920.2.a.j 1
3920.2.a.k 1
3920.2.a.l 1
3920.2.a.m 1
3920.2.a.n 1
3920.2.a.o 1
3920.2.a.p 1
3920.2.a.q 1
3920.2.a.r 1
3920.2.a.s 1
3920.2.a.t 1
3920.2.a.u 1
3920.2.a.v 1
3920.2.a.w 1
3920.2.a.x 1
3920.2.a.y 1
3920.2.a.z 1
3920.2.a.ba 1
3920.2.a.bb 1
3920.2.a.bc 1
3920.2.a.bd 1
3920.2.a.be 1
3920.2.a.bf 1
3920.2.a.bg 1
3920.2.a.bh 1
3920.2.a.bi 1
3920.2.a.bj 1
3920.2.a.bk 1
3920.2.a.bl 1
3920.2.a.bm 2
3920.2.a.bn 2
3920.2.a.bo 2
3920.2.a.bp 2
3920.2.a.bq 2
3920.2.a.br 2
3920.2.a.bs 2
3920.2.a.bt 2
3920.2.a.bu 2
3920.2.a.bv 2
3920.2.a.bw 2
3920.2.a.bx 2
3920.2.a.by 2
3920.2.a.bz 2
3920.2.a.ca 2
3920.2.a.cb 3
3920.2.a.cc 3
3920.2.a.cd 4
3920.2.a.ce 4
3920.2.b $$\chi_{3920}(1961, \cdot)$$ None 0 1
3920.2.e $$\chi_{3920}(3919, \cdot)$$ n/a 120 1
3920.2.g $$\chi_{3920}(1569, \cdot)$$ n/a 118 1
3920.2.h $$\chi_{3920}(391, \cdot)$$ None 0 1
3920.2.k $$\chi_{3920}(2351, \cdot)$$ 3920.2.k.a 8 1
3920.2.k.b 8
3920.2.k.c 8
3920.2.k.d 12
3920.2.k.e 12
3920.2.k.f 32
3920.2.l $$\chi_{3920}(3529, \cdot)$$ None 0 1
3920.2.n $$\chi_{3920}(1959, \cdot)$$ None 0 1
3920.2.q $$\chi_{3920}(961, \cdot)$$ n/a 160 2
3920.2.r $$\chi_{3920}(293, \cdot)$$ n/a 944 2
3920.2.t $$\chi_{3920}(1667, \cdot)$$ n/a 964 2
3920.2.w $$\chi_{3920}(1273, \cdot)$$ None 0 2
3920.2.x $$\chi_{3920}(687, \cdot)$$ n/a 246 2
3920.2.bb $$\chi_{3920}(589, \cdot)$$ n/a 964 2
3920.2.bc $$\chi_{3920}(1371, \cdot)$$ n/a 640 2
3920.2.bd $$\chi_{3920}(981, \cdot)$$ n/a 656 2
3920.2.be $$\chi_{3920}(979, \cdot)$$ n/a 944 2
3920.2.bi $$\chi_{3920}(1863, \cdot)$$ None 0 2
3920.2.bj $$\chi_{3920}(97, \cdot)$$ n/a 232 2
3920.2.bl $$\chi_{3920}(883, \cdot)$$ n/a 964 2
3920.2.bn $$\chi_{3920}(1077, \cdot)$$ n/a 944 2
3920.2.bq $$\chi_{3920}(999, \cdot)$$ None 0 2
3920.2.bs $$\chi_{3920}(31, \cdot)$$ n/a 160 2
3920.2.bv $$\chi_{3920}(569, \cdot)$$ None 0 2
3920.2.bw $$\chi_{3920}(2529, \cdot)$$ n/a 232 2
3920.2.bz $$\chi_{3920}(1991, \cdot)$$ None 0 2
3920.2.cb $$\chi_{3920}(361, \cdot)$$ None 0 2
3920.2.cc $$\chi_{3920}(1599, \cdot)$$ n/a 240 2
3920.2.ce $$\chi_{3920}(561, \cdot)$$ n/a 672 6
3920.2.cg $$\chi_{3920}(667, \cdot)$$ n/a 1888 4
3920.2.ci $$\chi_{3920}(117, \cdot)$$ n/a 1888 4
3920.2.cj $$\chi_{3920}(913, \cdot)$$ n/a 464 4
3920.2.cm $$\chi_{3920}(263, \cdot)$$ None 0 4
3920.2.cp $$\chi_{3920}(19, \cdot)$$ n/a 1888 4
3920.2.cq $$\chi_{3920}(1341, \cdot)$$ n/a 1280 4
3920.2.cr $$\chi_{3920}(411, \cdot)$$ n/a 1280 4
3920.2.cs $$\chi_{3920}(949, \cdot)$$ n/a 1888 4
3920.2.cv $$\chi_{3920}(863, \cdot)$$ n/a 480 4
3920.2.cy $$\chi_{3920}(313, \cdot)$$ None 0 4
3920.2.da $$\chi_{3920}(717, \cdot)$$ n/a 1888 4
3920.2.dc $$\chi_{3920}(67, \cdot)$$ n/a 1888 4
3920.2.de $$\chi_{3920}(279, \cdot)$$ None 0 6
3920.2.dg $$\chi_{3920}(169, \cdot)$$ None 0 6
3920.2.dj $$\chi_{3920}(111, \cdot)$$ n/a 672 6
3920.2.dk $$\chi_{3920}(951, \cdot)$$ None 0 6
3920.2.dn $$\chi_{3920}(449, \cdot)$$ n/a 996 6
3920.2.dp $$\chi_{3920}(559, \cdot)$$ n/a 1008 6
3920.2.dq $$\chi_{3920}(281, \cdot)$$ None 0 6
3920.2.ds $$\chi_{3920}(81, \cdot)$$ n/a 1344 12
3920.2.dt $$\chi_{3920}(13, \cdot)$$ n/a 8016 12
3920.2.dv $$\chi_{3920}(267, \cdot)$$ n/a 8016 12
3920.2.dx $$\chi_{3920}(183, \cdot)$$ None 0 12
3920.2.ea $$\chi_{3920}(433, \cdot)$$ n/a 1992 12
3920.2.ed $$\chi_{3920}(139, \cdot)$$ n/a 8016 12
3920.2.ee $$\chi_{3920}(141, \cdot)$$ n/a 5376 12
3920.2.ef $$\chi_{3920}(251, \cdot)$$ n/a 5376 12
3920.2.eg $$\chi_{3920}(29, \cdot)$$ n/a 8016 12
3920.2.ej $$\chi_{3920}(153, \cdot)$$ None 0 12
3920.2.em $$\chi_{3920}(127, \cdot)$$ n/a 2016 12
3920.2.en $$\chi_{3920}(43, \cdot)$$ n/a 8016 12
3920.2.ep $$\chi_{3920}(237, \cdot)$$ n/a 8016 12
3920.2.er $$\chi_{3920}(159, \cdot)$$ n/a 2016 12
3920.2.eu $$\chi_{3920}(121, \cdot)$$ None 0 12
3920.2.ew $$\chi_{3920}(311, \cdot)$$ None 0 12
3920.2.ex $$\chi_{3920}(289, \cdot)$$ n/a 1992 12
3920.2.fa $$\chi_{3920}(9, \cdot)$$ None 0 12
3920.2.fb $$\chi_{3920}(271, \cdot)$$ n/a 1344 12
3920.2.ff $$\chi_{3920}(199, \cdot)$$ None 0 12
3920.2.fh $$\chi_{3920}(123, \cdot)$$ n/a 16032 24
3920.2.fj $$\chi_{3920}(157, \cdot)$$ n/a 16032 24
3920.2.fl $$\chi_{3920}(207, \cdot)$$ n/a 4032 24
3920.2.fm $$\chi_{3920}(73, \cdot)$$ None 0 24
3920.2.fq $$\chi_{3920}(109, \cdot)$$ n/a 16032 24
3920.2.fr $$\chi_{3920}(131, \cdot)$$ n/a 10752 24
3920.2.fs $$\chi_{3920}(221, \cdot)$$ n/a 10752 24
3920.2.ft $$\chi_{3920}(59, \cdot)$$ n/a 16032 24
3920.2.fx $$\chi_{3920}(17, \cdot)$$ n/a 3984 24
3920.2.fy $$\chi_{3920}(23, \cdot)$$ None 0 24
3920.2.gb $$\chi_{3920}(173, \cdot)$$ n/a 16032 24
3920.2.gd $$\chi_{3920}(107, \cdot)$$ n/a 16032 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3920))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3920)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(560))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(980))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1960))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3920))$$$$^{\oplus 1}$$