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Properties

Label 3520.2
Level 3520
Weight 2
Dimension 185724
Nonzero newspaces 56
Sturm bound 1474560
Trace bound 97

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Defining parameters

Level: \( N \) = \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(1474560\)
Trace bound: \(97\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3520))\).

Total New Old
Modular forms 374400 188100 186300
Cusp forms 362881 185724 177157
Eisenstein series 11519 2376 9143

Trace form

\( 185724 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 192 q^{5} - 384 q^{6} - 104 q^{7} - 128 q^{8} - 172 q^{9} + O(q^{10}) \) \( 185724 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 192 q^{5} - 384 q^{6} - 104 q^{7} - 128 q^{8} - 172 q^{9} - 192 q^{10} - 332 q^{11} - 288 q^{12} - 160 q^{13} - 128 q^{14} - 156 q^{15} - 384 q^{16} - 256 q^{17} - 128 q^{18} - 128 q^{19} - 192 q^{20} - 368 q^{21} - 128 q^{22} - 224 q^{23} + 32 q^{24} - 208 q^{25} - 224 q^{26} - 72 q^{27} + 32 q^{28} - 64 q^{29} - 32 q^{30} - 200 q^{31} + 32 q^{32} - 56 q^{33} - 128 q^{34} - 140 q^{35} - 64 q^{36} - 96 q^{37} + 32 q^{38} - 88 q^{39} - 112 q^{40} - 480 q^{41} + 32 q^{42} - 144 q^{43} - 128 q^{44} - 440 q^{45} - 384 q^{46} - 168 q^{47} - 128 q^{48} - 260 q^{49} - 240 q^{50} - 184 q^{51} - 320 q^{52} - 224 q^{53} - 384 q^{54} - 100 q^{55} - 1088 q^{56} - 136 q^{57} - 416 q^{58} + 176 q^{59} - 384 q^{60} - 416 q^{61} - 256 q^{62} + 280 q^{63} - 512 q^{64} - 468 q^{65} - 592 q^{66} + 232 q^{67} - 320 q^{68} + 16 q^{69} - 384 q^{70} + 88 q^{71} - 416 q^{72} - 32 q^{73} - 352 q^{74} + 172 q^{75} - 640 q^{76} - 40 q^{77} - 384 q^{78} + 168 q^{79} - 112 q^{80} - 404 q^{81} + 192 q^{82} + 64 q^{83} + 320 q^{84} + 16 q^{85} + 32 q^{86} + 160 q^{87} + 16 q^{88} - 40 q^{89} + 96 q^{90} - 184 q^{91} + 480 q^{92} + 224 q^{93} + 256 q^{94} - 12 q^{95} + 160 q^{96} + 128 q^{97} + 416 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3520))\)

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
3520.2.a \(\chi_{3520}(1, \cdot)\) 3520.2.a.a 1 1
3520.2.a.b 1
3520.2.a.c 1
3520.2.a.d 1
3520.2.a.e 1
3520.2.a.f 1
3520.2.a.g 1
3520.2.a.h 1
3520.2.a.i 1
3520.2.a.j 1
3520.2.a.k 1
3520.2.a.l 1
3520.2.a.m 1
3520.2.a.n 1
3520.2.a.o 1
3520.2.a.p 1
3520.2.a.q 1
3520.2.a.r 1
3520.2.a.s 1
3520.2.a.t 1
3520.2.a.u 1
3520.2.a.v 1
3520.2.a.w 1
3520.2.a.x 1
3520.2.a.y 1
3520.2.a.z 1
3520.2.a.ba 1
3520.2.a.bb 1
3520.2.a.bc 1
3520.2.a.bd 1
3520.2.a.be 1
3520.2.a.bf 1
3520.2.a.bg 1
3520.2.a.bh 1
3520.2.a.bi 2
3520.2.a.bj 2
3520.2.a.bk 2
3520.2.a.bl 2
3520.2.a.bm 2
3520.2.a.bn 2
3520.2.a.bo 2
3520.2.a.bp 2
3520.2.a.bq 2
3520.2.a.br 2
3520.2.a.bs 2
3520.2.a.bt 2
3520.2.a.bu 3
3520.2.a.bv 3
3520.2.a.bw 3
3520.2.a.bx 3
3520.2.a.by 5
3520.2.a.bz 5
3520.2.b \(\chi_{3520}(1409, \cdot)\) n/a 120 1
3520.2.c \(\chi_{3520}(1759, \cdot)\) n/a 144 1
3520.2.f \(\chi_{3520}(2111, \cdot)\) 3520.2.f.a 2 1
3520.2.f.b 2
3520.2.f.c 2
3520.2.f.d 2
3520.2.f.e 4
3520.2.f.f 4
3520.2.f.g 4
3520.2.f.h 8
3520.2.f.i 8
3520.2.f.j 8
3520.2.f.k 12
3520.2.f.l 16
3520.2.f.m 24
3520.2.g \(\chi_{3520}(1761, \cdot)\) 3520.2.g.a 2 1
3520.2.g.b 2
3520.2.g.c 2
3520.2.g.d 2
3520.2.g.e 2
3520.2.g.f 2
3520.2.g.g 4
3520.2.g.h 4
3520.2.g.i 4
3520.2.g.j 4
3520.2.g.k 6
3520.2.g.l 6
3520.2.g.m 8
3520.2.g.n 8
3520.2.g.o 12
3520.2.g.p 12
3520.2.l \(\chi_{3520}(3169, \cdot)\) n/a 120 1
3520.2.m \(\chi_{3520}(3519, \cdot)\) n/a 140 1
3520.2.p \(\chi_{3520}(351, \cdot)\) 3520.2.p.a 4 1
3520.2.p.b 4
3520.2.p.c 12
3520.2.p.d 12
3520.2.p.e 32
3520.2.p.f 32
3520.2.s \(\chi_{3520}(463, \cdot)\) n/a 240 2
3520.2.t \(\chi_{3520}(593, \cdot)\) n/a 280 2
3520.2.v \(\chi_{3520}(1231, \cdot)\) n/a 192 2
3520.2.w \(\chi_{3520}(881, \cdot)\) n/a 160 2
3520.2.z \(\chi_{3520}(287, \cdot)\) n/a 240 2
3520.2.bb \(\chi_{3520}(417, \cdot)\) n/a 288 2
3520.2.bd \(\chi_{3520}(1473, \cdot)\) n/a 280 2
3520.2.bf \(\chi_{3520}(1343, \cdot)\) n/a 240 2
3520.2.bh \(\chi_{3520}(529, \cdot)\) n/a 240 2
3520.2.bi \(\chi_{3520}(879, \cdot)\) n/a 280 2
3520.2.bk \(\chi_{3520}(1167, \cdot)\) n/a 240 2
3520.2.bl \(\chi_{3520}(1297, \cdot)\) n/a 280 2
3520.2.bo \(\chi_{3520}(641, \cdot)\) n/a 384 4
3520.2.bp \(\chi_{3520}(727, \cdot)\) None 0 4
3520.2.bs \(\chi_{3520}(153, \cdot)\) None 0 4
3520.2.bt \(\chi_{3520}(439, \cdot)\) None 0 4
3520.2.bv \(\chi_{3520}(441, \cdot)\) None 0 4
3520.2.by \(\chi_{3520}(791, \cdot)\) None 0 4
3520.2.ca \(\chi_{3520}(89, \cdot)\) None 0 4
3520.2.cc \(\chi_{3520}(857, \cdot)\) None 0 4
3520.2.cd \(\chi_{3520}(23, \cdot)\) None 0 4
3520.2.cf \(\chi_{3520}(1311, \cdot)\) n/a 384 4
3520.2.ci \(\chi_{3520}(959, \cdot)\) n/a 560 4
3520.2.cj \(\chi_{3520}(289, \cdot)\) n/a 576 4
3520.2.co \(\chi_{3520}(801, \cdot)\) n/a 384 4
3520.2.cp \(\chi_{3520}(831, \cdot)\) n/a 384 4
3520.2.cs \(\chi_{3520}(479, \cdot)\) n/a 576 4
3520.2.ct \(\chi_{3520}(449, \cdot)\) n/a 560 4
3520.2.cv \(\chi_{3520}(197, \cdot)\) n/a 4576 8
3520.2.cx \(\chi_{3520}(67, \cdot)\) n/a 3840 8
3520.2.cz \(\chi_{3520}(309, \cdot)\) n/a 3840 8
3520.2.da \(\chi_{3520}(221, \cdot)\) n/a 2560 8
3520.2.dd \(\chi_{3520}(219, \cdot)\) n/a 4576 8
3520.2.de \(\chi_{3520}(131, \cdot)\) n/a 3072 8
3520.2.dg \(\chi_{3520}(373, \cdot)\) n/a 4576 8
3520.2.di \(\chi_{3520}(243, \cdot)\) n/a 3840 8
3520.2.dm \(\chi_{3520}(17, \cdot)\) n/a 1120 8
3520.2.dn \(\chi_{3520}(207, \cdot)\) n/a 1120 8
3520.2.do \(\chi_{3520}(79, \cdot)\) n/a 1120 8
3520.2.dr \(\chi_{3520}(49, \cdot)\) n/a 1120 8
3520.2.ds \(\chi_{3520}(193, \cdot)\) n/a 1120 8
3520.2.du \(\chi_{3520}(383, \cdot)\) n/a 1120 8
3520.2.dw \(\chi_{3520}(223, \cdot)\) n/a 1152 8
3520.2.dy \(\chi_{3520}(673, \cdot)\) n/a 1152 8
3520.2.ea \(\chi_{3520}(81, \cdot)\) n/a 768 8
3520.2.ed \(\chi_{3520}(271, \cdot)\) n/a 768 8
3520.2.ee \(\chi_{3520}(497, \cdot)\) n/a 1120 8
3520.2.ef \(\chi_{3520}(47, \cdot)\) n/a 1120 8
3520.2.ei \(\chi_{3520}(57, \cdot)\) None 0 16
3520.2.el \(\chi_{3520}(487, \cdot)\) None 0 16
3520.2.em \(\chi_{3520}(9, \cdot)\) None 0 16
3520.2.eo \(\chi_{3520}(151, \cdot)\) None 0 16
3520.2.er \(\chi_{3520}(201, \cdot)\) None 0 16
3520.2.et \(\chi_{3520}(39, \cdot)\) None 0 16
3520.2.ev \(\chi_{3520}(103, \cdot)\) None 0 16
3520.2.ew \(\chi_{3520}(457, \cdot)\) None 0 16
3520.2.ez \(\chi_{3520}(3, \cdot)\) n/a 18304 32
3520.2.fb \(\chi_{3520}(237, \cdot)\) n/a 18304 32
3520.2.fd \(\chi_{3520}(51, \cdot)\) n/a 12288 32
3520.2.fe \(\chi_{3520}(19, \cdot)\) n/a 18304 32
3520.2.fh \(\chi_{3520}(141, \cdot)\) n/a 12288 32
3520.2.fi \(\chi_{3520}(69, \cdot)\) n/a 18304 32
3520.2.fk \(\chi_{3520}(147, \cdot)\) n/a 18304 32
3520.2.fm \(\chi_{3520}(13, \cdot)\) n/a 18304 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1760))\)\(^{\oplus 2}\)