# Properties

 Label 3648.2 Level 3648 Weight 2 Dimension 153908 Nonzero newspaces 48 Sturm bound 1474560 Trace bound 51

## Defining parameters

 Level: $$N$$ = $$3648 = 2^{6} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$1474560$$ Trace bound: $$51$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3648))$$.

Total New Old
Modular forms 373824 155404 218420
Cusp forms 363457 153908 209549
Eisenstein series 10367 1496 8871

## Trace form

 $$153908 q - 96 q^{3} - 256 q^{4} - 128 q^{6} - 200 q^{7} - 160 q^{9} + O(q^{10})$$ $$153908 q - 96 q^{3} - 256 q^{4} - 128 q^{6} - 200 q^{7} - 160 q^{9} - 256 q^{10} - 16 q^{11} - 128 q^{12} - 288 q^{13} - 108 q^{15} - 256 q^{16} - 32 q^{17} - 128 q^{18} - 220 q^{19} - 120 q^{21} - 224 q^{22} - 48 q^{24} - 276 q^{25} + 160 q^{26} - 72 q^{27} - 96 q^{28} + 64 q^{29} + 32 q^{30} - 104 q^{31} + 160 q^{32} - 20 q^{33} - 96 q^{34} + 48 q^{35} + 32 q^{36} - 192 q^{37} + 80 q^{38} - 160 q^{39} - 96 q^{40} + 64 q^{41} - 48 q^{42} - 176 q^{43} + 32 q^{44} - 40 q^{45} - 256 q^{46} - 128 q^{48} - 420 q^{49} - 96 q^{50} + 36 q^{51} - 448 q^{52} - 160 q^{54} + 120 q^{55} - 224 q^{56} - 144 q^{57} - 832 q^{58} + 320 q^{59} - 320 q^{60} - 256 q^{61} - 192 q^{62} - 28 q^{63} - 640 q^{64} + 32 q^{65} - 288 q^{66} + 160 q^{67} - 192 q^{68} - 200 q^{69} - 640 q^{70} + 256 q^{71} - 128 q^{72} - 320 q^{73} - 224 q^{74} - 400 q^{76} - 96 q^{77} - 272 q^{78} - 104 q^{79} - 96 q^{80} - 352 q^{81} - 256 q^{82} - 80 q^{83} - 352 q^{84} - 352 q^{85} - 212 q^{87} - 256 q^{88} - 64 q^{89} - 416 q^{90} - 312 q^{91} - 240 q^{93} - 256 q^{94} - 48 q^{95} - 544 q^{96} - 288 q^{97} - 212 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3648))$$

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
3648.2.a $$\chi_{3648}(1, \cdot)$$ 3648.2.a.a 1 1
3648.2.a.b 1
3648.2.a.c 1
3648.2.a.d 1
3648.2.a.e 1
3648.2.a.f 1
3648.2.a.g 1
3648.2.a.h 1
3648.2.a.i 1
3648.2.a.j 1
3648.2.a.k 1
3648.2.a.l 1
3648.2.a.m 1
3648.2.a.n 1
3648.2.a.o 1
3648.2.a.p 1
3648.2.a.q 1
3648.2.a.r 1
3648.2.a.s 1
3648.2.a.t 1
3648.2.a.u 1
3648.2.a.v 1
3648.2.a.w 1
3648.2.a.x 1
3648.2.a.y 1
3648.2.a.z 1
3648.2.a.ba 1
3648.2.a.bb 1
3648.2.a.bc 1
3648.2.a.bd 1
3648.2.a.be 1
3648.2.a.bf 1
3648.2.a.bg 1
3648.2.a.bh 1
3648.2.a.bi 1
3648.2.a.bj 1
3648.2.a.bk 2
3648.2.a.bl 2
3648.2.a.bm 2
3648.2.a.bn 2
3648.2.a.bo 2
3648.2.a.bp 2
3648.2.a.bq 2
3648.2.a.br 2
3648.2.a.bs 2
3648.2.a.bt 2
3648.2.a.bu 2
3648.2.a.bv 2
3648.2.a.bw 3
3648.2.a.bx 3
3648.2.a.by 3
3648.2.a.bz 3
3648.2.d $$\chi_{3648}(191, \cdot)$$ n/a 144 1
3648.2.e $$\chi_{3648}(607, \cdot)$$ 3648.2.e.a 12 1
3648.2.e.b 12
3648.2.e.c 28
3648.2.e.d 28
3648.2.f $$\chi_{3648}(1025, \cdot)$$ n/a 156 1
3648.2.g $$\chi_{3648}(1825, \cdot)$$ 3648.2.g.a 4 1
3648.2.g.b 4
3648.2.g.c 4
3648.2.g.d 4
3648.2.g.e 4
3648.2.g.f 8
3648.2.g.g 8
3648.2.g.h 8
3648.2.g.i 12
3648.2.g.j 16
3648.2.j $$\chi_{3648}(2015, \cdot)$$ n/a 144 1
3648.2.k $$\chi_{3648}(2431, \cdot)$$ 3648.2.k.a 2 1
3648.2.k.b 2
3648.2.k.c 2
3648.2.k.d 2
3648.2.k.e 2
3648.2.k.f 2
3648.2.k.g 4
3648.2.k.h 4
3648.2.k.i 10
3648.2.k.j 10
3648.2.k.k 20
3648.2.k.l 20
3648.2.p $$\chi_{3648}(2849, \cdot)$$ n/a 160 1
3648.2.q $$\chi_{3648}(577, \cdot)$$ n/a 160 2
3648.2.r $$\chi_{3648}(113, \cdot)$$ n/a 312 2
3648.2.u $$\chi_{3648}(913, \cdot)$$ n/a 144 2
3648.2.v $$\chi_{3648}(1103, \cdot)$$ n/a 288 2
3648.2.y $$\chi_{3648}(1519, \cdot)$$ n/a 160 2
3648.2.bb $$\chi_{3648}(1471, \cdot)$$ n/a 160 2
3648.2.bc $$\chi_{3648}(2591, \cdot)$$ n/a 320 2
3648.2.bd $$\chi_{3648}(1889, \cdot)$$ n/a 320 2
3648.2.bg $$\chi_{3648}(31, \cdot)$$ n/a 160 2
3648.2.bh $$\chi_{3648}(767, \cdot)$$ n/a 312 2
3648.2.bm $$\chi_{3648}(2401, \cdot)$$ n/a 160 2
3648.2.bn $$\chi_{3648}(65, \cdot)$$ n/a 312 2
3648.2.bq $$\chi_{3648}(457, \cdot)$$ None 0 4
3648.2.br $$\chi_{3648}(151, \cdot)$$ None 0 4
3648.2.bs $$\chi_{3648}(647, \cdot)$$ None 0 4
3648.2.bt $$\chi_{3648}(569, \cdot)$$ None 0 4
3648.2.bw $$\chi_{3648}(385, \cdot)$$ n/a 480 6
3648.2.by $$\chi_{3648}(49, \cdot)$$ n/a 320 4
3648.2.bz $$\chi_{3648}(977, \cdot)$$ n/a 624 4
3648.2.cc $$\chi_{3648}(559, \cdot)$$ n/a 320 4
3648.2.cd $$\chi_{3648}(239, \cdot)$$ n/a 624 4
3648.2.cg $$\chi_{3648}(379, \cdot)$$ n/a 2560 8
3648.2.ch $$\chi_{3648}(229, \cdot)$$ n/a 2304 8
3648.2.cj $$\chi_{3648}(419, \cdot)$$ n/a 4608 8
3648.2.cm $$\chi_{3648}(341, \cdot)$$ n/a 5088 8
3648.2.cp $$\chi_{3648}(545, \cdot)$$ n/a 960 6
3648.2.cq $$\chi_{3648}(289, \cdot)$$ n/a 480 6
3648.2.cs $$\chi_{3648}(257, \cdot)$$ n/a 936 6
3648.2.cv $$\chi_{3648}(223, \cdot)$$ n/a 480 6
3648.2.cx $$\chi_{3648}(575, \cdot)$$ n/a 936 6
3648.2.cy $$\chi_{3648}(127, \cdot)$$ n/a 480 6
3648.2.da $$\chi_{3648}(479, \cdot)$$ n/a 960 6
3648.2.dc $$\chi_{3648}(521, \cdot)$$ None 0 8
3648.2.dd $$\chi_{3648}(311, \cdot)$$ None 0 8
3648.2.di $$\chi_{3648}(103, \cdot)$$ None 0 8
3648.2.dj $$\chi_{3648}(121, \cdot)$$ None 0 8
3648.2.dl $$\chi_{3648}(79, \cdot)$$ n/a 960 12
3648.2.dn $$\chi_{3648}(47, \cdot)$$ n/a 1872 12
3648.2.do $$\chi_{3648}(529, \cdot)$$ n/a 960 12
3648.2.dq $$\chi_{3648}(401, \cdot)$$ n/a 1872 12
3648.2.ds $$\chi_{3648}(259, \cdot)$$ n/a 5120 16
3648.2.dv $$\chi_{3648}(277, \cdot)$$ n/a 5120 16
3648.2.dx $$\chi_{3648}(11, \cdot)$$ n/a 10176 16
3648.2.dy $$\chi_{3648}(221, \cdot)$$ n/a 10176 16
3648.2.eb $$\chi_{3648}(25, \cdot)$$ None 0 24
3648.2.ec $$\chi_{3648}(295, \cdot)$$ None 0 24
3648.2.ee $$\chi_{3648}(41, \cdot)$$ None 0 24
3648.2.eh $$\chi_{3648}(23, \cdot)$$ None 0 24
3648.2.ei $$\chi_{3648}(29, \cdot)$$ n/a 30528 48
3648.2.ek $$\chi_{3648}(35, \cdot)$$ n/a 30528 48
3648.2.en $$\chi_{3648}(61, \cdot)$$ n/a 15360 48
3648.2.ep $$\chi_{3648}(67, \cdot)$$ n/a 15360 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3648))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3648)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1216))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1824))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3648))$$$$^{\oplus 1}$$