Properties

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

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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

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

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 the 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

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