Properties

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

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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

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

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

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