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Properties

Label 3920.2
Level 3920
Weight 2
Dimension 222134
Nonzero newspaces 56
Sturm bound 1806336
Trace bound 14

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Defining parameters

Level: \( N \) = \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(1806336\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3920))\).

Total New Old
Modular forms 458304 224752 233552
Cusp forms 444865 222134 222731
Eisenstein series 13439 2618 10821

Trace form

\( 222134 q - 124 q^{2} - 92 q^{3} - 128 q^{4} - 233 q^{5} - 384 q^{6} - 108 q^{7} - 232 q^{8} - 34 q^{9} + O(q^{10}) \) \( 222134 q - 124 q^{2} - 92 q^{3} - 128 q^{4} - 233 q^{5} - 384 q^{6} - 108 q^{7} - 232 q^{8} - 34 q^{9} - 188 q^{10} - 286 q^{11} - 120 q^{12} - 172 q^{13} - 144 q^{14} - 265 q^{15} - 360 q^{16} - 288 q^{17} - 132 q^{18} - 142 q^{19} - 192 q^{20} - 564 q^{21} - 224 q^{22} - 180 q^{23} - 128 q^{24} - 103 q^{25} - 384 q^{26} - 170 q^{27} - 144 q^{28} - 338 q^{29} - 152 q^{30} - 338 q^{31} - 104 q^{32} - 350 q^{33} - 72 q^{34} - 180 q^{35} - 592 q^{36} - 180 q^{37} - 48 q^{38} - 58 q^{39} - 100 q^{40} - 74 q^{41} - 148 q^{43} + 128 q^{44} - 129 q^{45} - 96 q^{46} - 56 q^{47} + 400 q^{48} - 228 q^{49} - 480 q^{50} - 186 q^{51} + 344 q^{52} + 36 q^{53} + 592 q^{54} - 77 q^{55} - 264 q^{56} + 290 q^{57} + 232 q^{58} - 22 q^{59} + 116 q^{60} - 258 q^{61} + 272 q^{62} - 48 q^{63} + 88 q^{64} - 389 q^{65} + 32 q^{66} + 8 q^{67} + 56 q^{68} - 30 q^{69} - 168 q^{70} - 562 q^{71} + 128 q^{72} - 148 q^{73} - 216 q^{74} - 137 q^{75} - 464 q^{76} - 276 q^{77} - 352 q^{78} - 170 q^{79} - 276 q^{80} - 1096 q^{81} - 192 q^{82} - 208 q^{83} - 144 q^{84} - 511 q^{85} - 440 q^{86} - 154 q^{87} - 232 q^{88} - 246 q^{89} - 448 q^{90} - 198 q^{91} - 264 q^{92} - 350 q^{93} - 440 q^{94} - 11 q^{95} - 888 q^{96} - 374 q^{97} - 312 q^{98} + 240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3920))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3920.2.a \(\chi_{3920}(1, \cdot)\) 3920.2.a.a 1 1
3920.2.a.b 1
3920.2.a.c 1
3920.2.a.d 1
3920.2.a.e 1
3920.2.a.f 1
3920.2.a.g 1
3920.2.a.h 1
3920.2.a.i 1
3920.2.a.j 1
3920.2.a.k 1
3920.2.a.l 1
3920.2.a.m 1
3920.2.a.n 1
3920.2.a.o 1
3920.2.a.p 1
3920.2.a.q 1
3920.2.a.r 1
3920.2.a.s 1
3920.2.a.t 1
3920.2.a.u 1
3920.2.a.v 1
3920.2.a.w 1
3920.2.a.x 1
3920.2.a.y 1
3920.2.a.z 1
3920.2.a.ba 1
3920.2.a.bb 1
3920.2.a.bc 1
3920.2.a.bd 1
3920.2.a.be 1
3920.2.a.bf 1
3920.2.a.bg 1
3920.2.a.bh 1
3920.2.a.bi 1
3920.2.a.bj 1
3920.2.a.bk 1
3920.2.a.bl 1
3920.2.a.bm 2
3920.2.a.bn 2
3920.2.a.bo 2
3920.2.a.bp 2
3920.2.a.bq 2
3920.2.a.br 2
3920.2.a.bs 2
3920.2.a.bt 2
3920.2.a.bu 2
3920.2.a.bv 2
3920.2.a.bw 2
3920.2.a.bx 2
3920.2.a.by 2
3920.2.a.bz 2
3920.2.a.ca 2
3920.2.a.cb 3
3920.2.a.cc 3
3920.2.a.cd 4
3920.2.a.ce 4
3920.2.b \(\chi_{3920}(1961, \cdot)\) None 0 1
3920.2.e \(\chi_{3920}(3919, \cdot)\) n/a 120 1
3920.2.g \(\chi_{3920}(1569, \cdot)\) n/a 118 1
3920.2.h \(\chi_{3920}(391, \cdot)\) None 0 1
3920.2.k \(\chi_{3920}(2351, \cdot)\) 3920.2.k.a 8 1
3920.2.k.b 8
3920.2.k.c 8
3920.2.k.d 12
3920.2.k.e 12
3920.2.k.f 32
3920.2.l \(\chi_{3920}(3529, \cdot)\) None 0 1
3920.2.n \(\chi_{3920}(1959, \cdot)\) None 0 1
3920.2.q \(\chi_{3920}(961, \cdot)\) n/a 160 2
3920.2.r \(\chi_{3920}(293, \cdot)\) n/a 944 2
3920.2.t \(\chi_{3920}(1667, \cdot)\) n/a 964 2
3920.2.w \(\chi_{3920}(1273, \cdot)\) None 0 2
3920.2.x \(\chi_{3920}(687, \cdot)\) n/a 246 2
3920.2.bb \(\chi_{3920}(589, \cdot)\) n/a 964 2
3920.2.bc \(\chi_{3920}(1371, \cdot)\) n/a 640 2
3920.2.bd \(\chi_{3920}(981, \cdot)\) n/a 656 2
3920.2.be \(\chi_{3920}(979, \cdot)\) n/a 944 2
3920.2.bi \(\chi_{3920}(1863, \cdot)\) None 0 2
3920.2.bj \(\chi_{3920}(97, \cdot)\) n/a 232 2
3920.2.bl \(\chi_{3920}(883, \cdot)\) n/a 964 2
3920.2.bn \(\chi_{3920}(1077, \cdot)\) n/a 944 2
3920.2.bq \(\chi_{3920}(999, \cdot)\) None 0 2
3920.2.bs \(\chi_{3920}(31, \cdot)\) n/a 160 2
3920.2.bv \(\chi_{3920}(569, \cdot)\) None 0 2
3920.2.bw \(\chi_{3920}(2529, \cdot)\) n/a 232 2
3920.2.bz \(\chi_{3920}(1991, \cdot)\) None 0 2
3920.2.cb \(\chi_{3920}(361, \cdot)\) None 0 2
3920.2.cc \(\chi_{3920}(1599, \cdot)\) n/a 240 2
3920.2.ce \(\chi_{3920}(561, \cdot)\) n/a 672 6
3920.2.cg \(\chi_{3920}(667, \cdot)\) n/a 1888 4
3920.2.ci \(\chi_{3920}(117, \cdot)\) n/a 1888 4
3920.2.cj \(\chi_{3920}(913, \cdot)\) n/a 464 4
3920.2.cm \(\chi_{3920}(263, \cdot)\) None 0 4
3920.2.cp \(\chi_{3920}(19, \cdot)\) n/a 1888 4
3920.2.cq \(\chi_{3920}(1341, \cdot)\) n/a 1280 4
3920.2.cr \(\chi_{3920}(411, \cdot)\) n/a 1280 4
3920.2.cs \(\chi_{3920}(949, \cdot)\) n/a 1888 4
3920.2.cv \(\chi_{3920}(863, \cdot)\) n/a 480 4
3920.2.cy \(\chi_{3920}(313, \cdot)\) None 0 4
3920.2.da \(\chi_{3920}(717, \cdot)\) n/a 1888 4
3920.2.dc \(\chi_{3920}(67, \cdot)\) n/a 1888 4
3920.2.de \(\chi_{3920}(279, \cdot)\) None 0 6
3920.2.dg \(\chi_{3920}(169, \cdot)\) None 0 6
3920.2.dj \(\chi_{3920}(111, \cdot)\) n/a 672 6
3920.2.dk \(\chi_{3920}(951, \cdot)\) None 0 6
3920.2.dn \(\chi_{3920}(449, \cdot)\) n/a 996 6
3920.2.dp \(\chi_{3920}(559, \cdot)\) n/a 1008 6
3920.2.dq \(\chi_{3920}(281, \cdot)\) None 0 6
3920.2.ds \(\chi_{3920}(81, \cdot)\) n/a 1344 12
3920.2.dt \(\chi_{3920}(13, \cdot)\) n/a 8016 12
3920.2.dv \(\chi_{3920}(267, \cdot)\) n/a 8016 12
3920.2.dx \(\chi_{3920}(183, \cdot)\) None 0 12
3920.2.ea \(\chi_{3920}(433, \cdot)\) n/a 1992 12
3920.2.ed \(\chi_{3920}(139, \cdot)\) n/a 8016 12
3920.2.ee \(\chi_{3920}(141, \cdot)\) n/a 5376 12
3920.2.ef \(\chi_{3920}(251, \cdot)\) n/a 5376 12
3920.2.eg \(\chi_{3920}(29, \cdot)\) n/a 8016 12
3920.2.ej \(\chi_{3920}(153, \cdot)\) None 0 12
3920.2.em \(\chi_{3920}(127, \cdot)\) n/a 2016 12
3920.2.en \(\chi_{3920}(43, \cdot)\) n/a 8016 12
3920.2.ep \(\chi_{3920}(237, \cdot)\) n/a 8016 12
3920.2.er \(\chi_{3920}(159, \cdot)\) n/a 2016 12
3920.2.eu \(\chi_{3920}(121, \cdot)\) None 0 12
3920.2.ew \(\chi_{3920}(311, \cdot)\) None 0 12
3920.2.ex \(\chi_{3920}(289, \cdot)\) n/a 1992 12
3920.2.fa \(\chi_{3920}(9, \cdot)\) None 0 12
3920.2.fb \(\chi_{3920}(271, \cdot)\) n/a 1344 12
3920.2.ff \(\chi_{3920}(199, \cdot)\) None 0 12
3920.2.fh \(\chi_{3920}(123, \cdot)\) n/a 16032 24
3920.2.fj \(\chi_{3920}(157, \cdot)\) n/a 16032 24
3920.2.fl \(\chi_{3920}(207, \cdot)\) n/a 4032 24
3920.2.fm \(\chi_{3920}(73, \cdot)\) None 0 24
3920.2.fq \(\chi_{3920}(109, \cdot)\) n/a 16032 24
3920.2.fr \(\chi_{3920}(131, \cdot)\) n/a 10752 24
3920.2.fs \(\chi_{3920}(221, \cdot)\) n/a 10752 24
3920.2.ft \(\chi_{3920}(59, \cdot)\) n/a 16032 24
3920.2.fx \(\chi_{3920}(17, \cdot)\) n/a 3984 24
3920.2.fy \(\chi_{3920}(23, \cdot)\) None 0 24
3920.2.gb \(\chi_{3920}(173, \cdot)\) n/a 16032 24
3920.2.gd \(\chi_{3920}(107, \cdot)\) n/a 16032 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1960))\)\(^{\oplus 2}\)