Properties

Label 3960.2
Level 3960
Weight 2
Dimension 165496
Nonzero newspaces 72
Sturm bound 1658880
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(1658880\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3960))\).

Total New Old
Modular forms 422400 167440 254960
Cusp forms 407041 165496 241545
Eisenstein series 15359 1944 13415

Trace form

\( 165496 q - 44 q^{2} - 60 q^{3} - 44 q^{4} + 10 q^{5} - 208 q^{6} - 36 q^{7} - 92 q^{8} - 132 q^{9} + O(q^{10}) \) \( 165496 q - 44 q^{2} - 60 q^{3} - 44 q^{4} + 10 q^{5} - 208 q^{6} - 36 q^{7} - 92 q^{8} - 132 q^{9} - 246 q^{10} - 186 q^{11} - 184 q^{12} - 4 q^{13} - 116 q^{14} - 136 q^{15} - 204 q^{16} - 136 q^{17} - 48 q^{18} - 198 q^{19} - 86 q^{20} - 64 q^{21} - 40 q^{22} - 220 q^{23} + 48 q^{24} - 162 q^{25} - 52 q^{26} - 96 q^{27} - 68 q^{28} - 40 q^{29} + 4 q^{30} - 256 q^{31} + 136 q^{32} - 166 q^{33} - 168 q^{34} - 144 q^{35} + 24 q^{36} - 52 q^{37} + 120 q^{38} + 64 q^{39} - 36 q^{40} - 372 q^{41} + 200 q^{42} - 64 q^{43} - 28 q^{44} + 4 q^{45} - 360 q^{46} + 112 q^{47} + 144 q^{48} - 274 q^{49} + 180 q^{50} - 64 q^{51} + 32 q^{52} - 92 q^{53} + 112 q^{54} - 276 q^{55} - 184 q^{56} - 276 q^{57} + 192 q^{58} + 30 q^{59} + 20 q^{60} - 108 q^{61} + 68 q^{62} + 64 q^{63} + 124 q^{64} - 172 q^{65} - 304 q^{66} - 212 q^{67} - 4 q^{68} - 24 q^{69} + 224 q^{70} - 156 q^{71} - 296 q^{72} - 480 q^{73} - 120 q^{74} + 104 q^{75} - 60 q^{76} - 228 q^{77} - 360 q^{78} - 300 q^{79} + 52 q^{80} - 260 q^{81} + 236 q^{82} + 54 q^{83} - 240 q^{84} - 160 q^{85} - 84 q^{86} + 232 q^{87} + 296 q^{88} - 112 q^{89} - 116 q^{90} - 608 q^{91} + 236 q^{92} + 152 q^{93} + 228 q^{94} + 158 q^{95} + 136 q^{96} - 118 q^{97} + 312 q^{98} + 148 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3960))\)

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
3960.2.a \(\chi_{3960}(1, \cdot)\) 3960.2.a.a 1 1
3960.2.a.b 1
3960.2.a.c 1
3960.2.a.d 1
3960.2.a.e 1
3960.2.a.f 1
3960.2.a.g 1
3960.2.a.h 1
3960.2.a.i 1
3960.2.a.j 1
3960.2.a.k 1
3960.2.a.l 1
3960.2.a.m 1
3960.2.a.n 1
3960.2.a.o 1
3960.2.a.p 1
3960.2.a.q 1
3960.2.a.r 1
3960.2.a.s 1
3960.2.a.t 1
3960.2.a.u 2
3960.2.a.v 2
3960.2.a.w 2
3960.2.a.x 2
3960.2.a.y 2
3960.2.a.z 2
3960.2.a.ba 2
3960.2.a.bb 2
3960.2.a.bc 2
3960.2.a.bd 2
3960.2.a.be 2
3960.2.a.bf 2
3960.2.a.bg 3
3960.2.a.bh 3
3960.2.d \(\chi_{3960}(3169, \cdot)\) 3960.2.d.a 2 1
3960.2.d.b 2
3960.2.d.c 2
3960.2.d.d 6
3960.2.d.e 6
3960.2.d.f 8
3960.2.d.g 10
3960.2.d.h 10
3960.2.d.i 14
3960.2.d.j 14
3960.2.e \(\chi_{3960}(3851, \cdot)\) n/a 160 1
3960.2.f \(\chi_{3960}(3761, \cdot)\) 3960.2.f.a 12 1
3960.2.f.b 12
3960.2.f.c 12
3960.2.f.d 12
3960.2.g \(\chi_{3960}(1099, \cdot)\) n/a 356 1
3960.2.j \(\chi_{3960}(1189, \cdot)\) n/a 300 1
3960.2.k \(\chi_{3960}(1871, \cdot)\) None 0 1
3960.2.p \(\chi_{3960}(1781, \cdot)\) n/a 192 1
3960.2.q \(\chi_{3960}(3079, \cdot)\) None 0 1
3960.2.t \(\chi_{3960}(3871, \cdot)\) None 0 1
3960.2.u \(\chi_{3960}(989, \cdot)\) n/a 288 1
3960.2.v \(\chi_{3960}(1079, \cdot)\) None 0 1
3960.2.w \(\chi_{3960}(1981, \cdot)\) n/a 200 1
3960.2.z \(\chi_{3960}(1891, \cdot)\) n/a 240 1
3960.2.ba \(\chi_{3960}(2969, \cdot)\) 3960.2.ba.a 4 1
3960.2.ba.b 4
3960.2.ba.c 64
3960.2.bf \(\chi_{3960}(3059, \cdot)\) n/a 240 1
3960.2.bg \(\chi_{3960}(1321, \cdot)\) n/a 240 2
3960.2.bi \(\chi_{3960}(1583, \cdot)\) None 0 2
3960.2.bj \(\chi_{3960}(1693, \cdot)\) n/a 712 2
3960.2.bm \(\chi_{3960}(1387, \cdot)\) n/a 600 2
3960.2.bn \(\chi_{3960}(1673, \cdot)\) n/a 120 2
3960.2.bq \(\chi_{3960}(1783, \cdot)\) None 0 2
3960.2.br \(\chi_{3960}(1277, \cdot)\) n/a 480 2
3960.2.bu \(\chi_{3960}(1187, \cdot)\) n/a 576 2
3960.2.bv \(\chi_{3960}(1297, \cdot)\) n/a 180 2
3960.2.bx \(\chi_{3960}(361, \cdot)\) n/a 240 4
3960.2.by \(\chi_{3960}(329, \cdot)\) n/a 432 2
3960.2.bz \(\chi_{3960}(571, \cdot)\) n/a 1152 2
3960.2.ce \(\chi_{3960}(419, \cdot)\) n/a 1440 2
3960.2.ch \(\chi_{3960}(2309, \cdot)\) n/a 1712 2
3960.2.ci \(\chi_{3960}(1231, \cdot)\) None 0 2
3960.2.cj \(\chi_{3960}(661, \cdot)\) n/a 960 2
3960.2.ck \(\chi_{3960}(2399, \cdot)\) None 0 2
3960.2.cn \(\chi_{3960}(551, \cdot)\) None 0 2
3960.2.co \(\chi_{3960}(2509, \cdot)\) n/a 1440 2
3960.2.ct \(\chi_{3960}(439, \cdot)\) None 0 2
3960.2.cu \(\chi_{3960}(461, \cdot)\) n/a 1152 2
3960.2.cx \(\chi_{3960}(1211, \cdot)\) n/a 960 2
3960.2.cy \(\chi_{3960}(529, \cdot)\) n/a 360 2
3960.2.cz \(\chi_{3960}(2419, \cdot)\) n/a 1712 2
3960.2.da \(\chi_{3960}(1121, \cdot)\) n/a 288 2
3960.2.dd \(\chi_{3960}(179, \cdot)\) n/a 1152 4
3960.2.di \(\chi_{3960}(811, \cdot)\) n/a 960 4
3960.2.dj \(\chi_{3960}(809, \cdot)\) n/a 288 4
3960.2.dm \(\chi_{3960}(719, \cdot)\) None 0 4
3960.2.dn \(\chi_{3960}(181, \cdot)\) n/a 960 4
3960.2.do \(\chi_{3960}(271, \cdot)\) None 0 4
3960.2.dp \(\chi_{3960}(629, \cdot)\) n/a 1152 4
3960.2.ds \(\chi_{3960}(701, \cdot)\) n/a 768 4
3960.2.dt \(\chi_{3960}(919, \cdot)\) None 0 4
3960.2.dy \(\chi_{3960}(829, \cdot)\) n/a 1424 4
3960.2.dz \(\chi_{3960}(71, \cdot)\) None 0 4
3960.2.ec \(\chi_{3960}(161, \cdot)\) n/a 192 4
3960.2.ed \(\chi_{3960}(19, \cdot)\) n/a 1424 4
3960.2.ee \(\chi_{3960}(289, \cdot)\) n/a 360 4
3960.2.ef \(\chi_{3960}(251, \cdot)\) n/a 768 4
3960.2.ej \(\chi_{3960}(353, \cdot)\) n/a 720 4
3960.2.ek \(\chi_{3960}(67, \cdot)\) n/a 2880 4
3960.2.en \(\chi_{3960}(373, \cdot)\) n/a 3424 4
3960.2.eo \(\chi_{3960}(263, \cdot)\) None 0 4
3960.2.er \(\chi_{3960}(1033, \cdot)\) n/a 864 4
3960.2.es \(\chi_{3960}(923, \cdot)\) n/a 3424 4
3960.2.ev \(\chi_{3960}(1013, \cdot)\) n/a 2880 4
3960.2.ew \(\chi_{3960}(463, \cdot)\) None 0 4
3960.2.ey \(\chi_{3960}(841, \cdot)\) n/a 1152 8
3960.2.fa \(\chi_{3960}(73, \cdot)\) n/a 720 8
3960.2.fb \(\chi_{3960}(107, \cdot)\) n/a 2304 8
3960.2.fe \(\chi_{3960}(53, \cdot)\) n/a 2304 8
3960.2.ff \(\chi_{3960}(487, \cdot)\) None 0 8
3960.2.fi \(\chi_{3960}(377, \cdot)\) n/a 576 8
3960.2.fj \(\chi_{3960}(163, \cdot)\) n/a 2848 8
3960.2.fm \(\chi_{3960}(613, \cdot)\) n/a 2848 8
3960.2.fn \(\chi_{3960}(503, \cdot)\) None 0 8
3960.2.fr \(\chi_{3960}(139, \cdot)\) n/a 6848 8
3960.2.fs \(\chi_{3960}(41, \cdot)\) n/a 1152 8
3960.2.ft \(\chi_{3960}(731, \cdot)\) n/a 4608 8
3960.2.fu \(\chi_{3960}(49, \cdot)\) n/a 1728 8
3960.2.fx \(\chi_{3960}(79, \cdot)\) None 0 8
3960.2.fy \(\chi_{3960}(101, \cdot)\) n/a 4608 8
3960.2.gd \(\chi_{3960}(191, \cdot)\) None 0 8
3960.2.ge \(\chi_{3960}(229, \cdot)\) n/a 6848 8
3960.2.gh \(\chi_{3960}(301, \cdot)\) n/a 4608 8
3960.2.gi \(\chi_{3960}(119, \cdot)\) None 0 8
3960.2.gj \(\chi_{3960}(29, \cdot)\) n/a 6848 8
3960.2.gk \(\chi_{3960}(151, \cdot)\) None 0 8
3960.2.gn \(\chi_{3960}(59, \cdot)\) n/a 6848 8
3960.2.gs \(\chi_{3960}(569, \cdot)\) n/a 1728 8
3960.2.gt \(\chi_{3960}(211, \cdot)\) n/a 4608 8
3960.2.gv \(\chi_{3960}(103, \cdot)\) None 0 16
3960.2.gw \(\chi_{3960}(317, \cdot)\) n/a 13696 16
3960.2.gz \(\chi_{3960}(83, \cdot)\) n/a 13696 16
3960.2.ha \(\chi_{3960}(193, \cdot)\) n/a 3456 16
3960.2.hd \(\chi_{3960}(167, \cdot)\) None 0 16
3960.2.he \(\chi_{3960}(13, \cdot)\) n/a 13696 16
3960.2.hh \(\chi_{3960}(427, \cdot)\) n/a 13696 16
3960.2.hi \(\chi_{3960}(113, \cdot)\) n/a 3456 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1980))\)\(^{\oplus 2}\)