# Properties

 Label 3840.2 Level 3840 Weight 2 Dimension 151440 Nonzero newspaces 44 Sturm bound 1572864 Trace bound 169

## Defining parameters

 Level: $$N$$ = $$3840 = 2^{8} \cdot 3 \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$44$$ Sturm bound: $$1572864$$ Trace bound: $$169$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3840))$$.

Total New Old
Modular forms 398848 152688 246160
Cusp forms 387585 151440 236145
Eisenstein series 11263 1248 10015

## Trace form

 $$151440 q - 48 q^{3} - 128 q^{4} - 192 q^{6} - 96 q^{7} - 80 q^{9} + O(q^{10})$$ $$151440 q - 48 q^{3} - 128 q^{4} - 192 q^{6} - 96 q^{7} - 80 q^{9} - 192 q^{10} - 64 q^{12} - 128 q^{13} - 72 q^{15} - 384 q^{16} - 64 q^{18} - 96 q^{19} - 192 q^{21} - 128 q^{22} - 64 q^{24} - 240 q^{25} - 48 q^{27} - 128 q^{28} - 96 q^{30} - 320 q^{31} - 112 q^{33} - 128 q^{34} - 192 q^{36} - 128 q^{37} - 48 q^{39} - 192 q^{40} - 64 q^{42} - 96 q^{43} - 96 q^{45} - 384 q^{46} - 64 q^{48} - 304 q^{49} - 208 q^{51} - 128 q^{52} - 128 q^{53} - 64 q^{54} - 272 q^{55} - 208 q^{57} - 128 q^{58} - 256 q^{59} - 96 q^{60} - 640 q^{61} - 96 q^{63} - 128 q^{64} - 128 q^{65} - 192 q^{66} - 416 q^{67} - 192 q^{69} - 192 q^{70} - 256 q^{71} - 64 q^{72} - 416 q^{73} - 136 q^{75} - 384 q^{76} - 128 q^{77} - 64 q^{78} - 224 q^{79} - 288 q^{81} - 128 q^{82} - 64 q^{84} - 272 q^{85} - 48 q^{87} - 128 q^{88} - 96 q^{90} - 288 q^{91} + 32 q^{93} - 128 q^{94} - 192 q^{96} - 224 q^{97} - 48 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3840))$$

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
3840.2.a $$\chi_{3840}(1, \cdot)$$ 3840.2.a.a 1 1
3840.2.a.b 1
3840.2.a.c 1
3840.2.a.d 1
3840.2.a.e 1
3840.2.a.f 1
3840.2.a.g 1
3840.2.a.h 1
3840.2.a.i 1
3840.2.a.j 1
3840.2.a.k 1
3840.2.a.l 1
3840.2.a.m 1
3840.2.a.n 1
3840.2.a.o 1
3840.2.a.p 1
3840.2.a.q 1
3840.2.a.r 1
3840.2.a.s 1
3840.2.a.t 1
3840.2.a.u 1
3840.2.a.v 1
3840.2.a.w 1
3840.2.a.x 1
3840.2.a.y 1
3840.2.a.z 1
3840.2.a.ba 1
3840.2.a.bb 1
3840.2.a.bc 2
3840.2.a.bd 2
3840.2.a.be 2
3840.2.a.bf 2
3840.2.a.bg 2
3840.2.a.bh 2
3840.2.a.bi 2
3840.2.a.bj 2
3840.2.a.bk 2
3840.2.a.bl 2
3840.2.a.bm 2
3840.2.a.bn 2
3840.2.a.bo 3
3840.2.a.bp 3
3840.2.a.bq 3
3840.2.a.br 3
3840.2.b $$\chi_{3840}(1151, \cdot)$$ n/a 128 1
3840.2.d $$\chi_{3840}(2689, \cdot)$$ 3840.2.d.a 2 1
3840.2.d.b 2
3840.2.d.c 2
3840.2.d.d 2
3840.2.d.e 2
3840.2.d.f 2
3840.2.d.g 2
3840.2.d.h 2
3840.2.d.i 2
3840.2.d.j 2
3840.2.d.k 2
3840.2.d.l 2
3840.2.d.m 2
3840.2.d.n 2
3840.2.d.o 2
3840.2.d.p 2
3840.2.d.q 2
3840.2.d.r 2
3840.2.d.s 2
3840.2.d.t 2
3840.2.d.u 2
3840.2.d.v 2
3840.2.d.w 2
3840.2.d.x 2
3840.2.d.y 2
3840.2.d.z 2
3840.2.d.ba 2
3840.2.d.bb 2
3840.2.d.bc 2
3840.2.d.bd 2
3840.2.d.be 2
3840.2.d.bf 2
3840.2.d.bg 4
3840.2.d.bh 4
3840.2.d.bi 6
3840.2.d.bj 6
3840.2.d.bk 6
3840.2.d.bl 6
3840.2.f $$\chi_{3840}(769, \cdot)$$ 3840.2.f.a 2 1
3840.2.f.b 2
3840.2.f.c 2
3840.2.f.d 2
3840.2.f.e 6
3840.2.f.f 6
3840.2.f.g 6
3840.2.f.h 6
3840.2.f.i 8
3840.2.f.j 8
3840.2.f.k 8
3840.2.f.l 12
3840.2.f.m 12
3840.2.f.n 16
3840.2.h $$\chi_{3840}(3071, \cdot)$$ n/a 128 1
3840.2.k $$\chi_{3840}(1921, \cdot)$$ 3840.2.k.a 2 1
3840.2.k.b 2
3840.2.k.c 2
3840.2.k.d 2
3840.2.k.e 2
3840.2.k.f 2
3840.2.k.g 2
3840.2.k.h 2
3840.2.k.i 2
3840.2.k.j 2
3840.2.k.k 2
3840.2.k.l 2
3840.2.k.m 2
3840.2.k.n 2
3840.2.k.o 2
3840.2.k.p 2
3840.2.k.q 2
3840.2.k.r 2
3840.2.k.s 2
3840.2.k.t 2
3840.2.k.u 2
3840.2.k.v 2
3840.2.k.w 2
3840.2.k.x 2
3840.2.k.y 2
3840.2.k.z 2
3840.2.k.ba 2
3840.2.k.bb 2
3840.2.k.bc 4
3840.2.k.bd 4
3840.2.m $$\chi_{3840}(1919, \cdot)$$ n/a 184 1
3840.2.o $$\chi_{3840}(3839, \cdot)$$ n/a 184 1
3840.2.s $$\chi_{3840}(961, \cdot)$$ n/a 128 2
3840.2.t $$\chi_{3840}(959, \cdot)$$ n/a 384 2
3840.2.v $$\chi_{3840}(257, \cdot)$$ n/a 368 2
3840.2.w $$\chi_{3840}(2047, \cdot)$$ n/a 192 2
3840.2.y $$\chi_{3840}(703, \cdot)$$ n/a 192 2
3840.2.bb $$\chi_{3840}(833, \cdot)$$ n/a 384 2
3840.2.bc $$\chi_{3840}(2623, \cdot)$$ n/a 192 2
3840.2.bf $$\chi_{3840}(2753, \cdot)$$ n/a 384 2
3840.2.bh $$\chi_{3840}(127, \cdot)$$ n/a 192 2
3840.2.bi $$\chi_{3840}(2177, \cdot)$$ n/a 368 2
3840.2.bk $$\chi_{3840}(191, \cdot)$$ n/a 256 2
3840.2.bl $$\chi_{3840}(1729, \cdot)$$ n/a 192 2
3840.2.bo $$\chi_{3840}(607, \cdot)$$ n/a 384 4
3840.2.br $$\chi_{3840}(737, \cdot)$$ n/a 736 4
3840.2.bs $$\chi_{3840}(479, \cdot)$$ n/a 736 4
3840.2.bv $$\chi_{3840}(481, \cdot)$$ n/a 256 4
3840.2.bx $$\chi_{3840}(671, \cdot)$$ n/a 512 4
3840.2.by $$\chi_{3840}(289, \cdot)$$ n/a 384 4
3840.2.cb $$\chi_{3840}(353, \cdot)$$ n/a 736 4
3840.2.cc $$\chi_{3840}(223, \cdot)$$ n/a 384 4
3840.2.cf $$\chi_{3840}(497, \cdot)$$ n/a 1504 8
3840.2.cg $$\chi_{3840}(367, \cdot)$$ n/a 768 8
3840.2.ci $$\chi_{3840}(241, \cdot)$$ n/a 512 8
3840.2.ck $$\chi_{3840}(49, \cdot)$$ n/a 768 8
3840.2.cn $$\chi_{3840}(431, \cdot)$$ n/a 1024 8
3840.2.cp $$\chi_{3840}(239, \cdot)$$ n/a 1504 8
3840.2.cr $$\chi_{3840}(17, \cdot)$$ n/a 1504 8
3840.2.cs $$\chi_{3840}(847, \cdot)$$ n/a 768 8
3840.2.cw $$\chi_{3840}(233, \cdot)$$ None 0 16
3840.2.cx $$\chi_{3840}(7, \cdot)$$ None 0 16
3840.2.cy $$\chi_{3840}(71, \cdot)$$ None 0 16
3840.2.cz $$\chi_{3840}(169, \cdot)$$ None 0 16
3840.2.dc $$\chi_{3840}(121, \cdot)$$ None 0 16
3840.2.dd $$\chi_{3840}(119, \cdot)$$ None 0 16
3840.2.di $$\chi_{3840}(103, \cdot)$$ None 0 16
3840.2.dj $$\chi_{3840}(137, \cdot)$$ None 0 16
3840.2.dm $$\chi_{3840}(61, \cdot)$$ n/a 8192 32
3840.2.dn $$\chi_{3840}(59, \cdot)$$ n/a 24448 32
3840.2.do $$\chi_{3840}(43, \cdot)$$ n/a 12288 32
3840.2.dr $$\chi_{3840}(53, \cdot)$$ n/a 24448 32
3840.2.ds $$\chi_{3840}(163, \cdot)$$ n/a 12288 32
3840.2.dv $$\chi_{3840}(173, \cdot)$$ n/a 24448 32
3840.2.dw $$\chi_{3840}(11, \cdot)$$ n/a 16384 32
3840.2.dx $$\chi_{3840}(109, \cdot)$$ n/a 12288 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3840))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3840)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(384))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(480))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(640))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(768))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(960))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1280))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1920))$$$$^{\oplus 2}$$