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Properties

Label 2160.4
Level 2160
Weight 4
Dimension 151632
Nonzero newspaces 42
Sturm bound 995328
Trace bound 31

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Defining parameters

Level: \( N \) = \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(995328\)
Trace bound: \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2160))\).

Total New Old
Modular forms 376608 152496 224112
Cusp forms 369888 151632 218256
Eisenstein series 6720 864 5856

Trace form

\( 151632 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 59 q^{5} - 144 q^{6} - 6 q^{7} - 32 q^{8} - 12 q^{9} + O(q^{10}) \) \( 151632 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 59 q^{5} - 144 q^{6} - 6 q^{7} - 32 q^{8} - 12 q^{9} - 84 q^{10} - 206 q^{11} - 48 q^{12} - 142 q^{13} - 96 q^{14} - 54 q^{15} - 696 q^{16} - 234 q^{17} - 48 q^{18} + 162 q^{19} + 260 q^{20} - 180 q^{21} + 952 q^{22} + 242 q^{23} - 48 q^{24} + 315 q^{25} + 992 q^{26} - 1368 q^{27} + 16 q^{28} - 826 q^{29} - 72 q^{30} + 270 q^{31} - 1992 q^{32} + 1284 q^{33} - 1448 q^{34} + 1319 q^{35} - 144 q^{36} + 1538 q^{37} + 2376 q^{38} + 1620 q^{39} + 204 q^{40} + 418 q^{41} - 48 q^{42} + 1194 q^{43} - 3112 q^{44} - 1410 q^{45} - 2920 q^{46} - 2302 q^{47} - 48 q^{48} - 1628 q^{49} - 2212 q^{50} + 54 q^{51} - 1784 q^{52} + 784 q^{53} - 48 q^{54} + 1150 q^{55} + 15624 q^{56} + 6498 q^{57} + 18184 q^{58} + 2102 q^{59} + 7248 q^{60} + 4614 q^{61} + 12304 q^{62} + 24 q^{63} - 2216 q^{64} - 3105 q^{65} - 14904 q^{66} - 2478 q^{67} - 30200 q^{68} - 12540 q^{69} - 13332 q^{70} - 9962 q^{71} - 23904 q^{72} - 8174 q^{73} - 36432 q^{74} - 2532 q^{75} - 19752 q^{76} - 17214 q^{77} - 9096 q^{78} + 1482 q^{79} + 4892 q^{80} + 3324 q^{81} + 12448 q^{82} + 6746 q^{83} + 22392 q^{84} + 5093 q^{85} + 54984 q^{86} + 6048 q^{87} + 22552 q^{88} + 25474 q^{89} + 8676 q^{90} - 6230 q^{91} - 12136 q^{92} + 14772 q^{93} - 9112 q^{94} + 817 q^{95} - 144 q^{96} + 2802 q^{97} - 9328 q^{98} - 7596 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2160))\)

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
2160.4.a \(\chi_{2160}(1, \cdot)\) 2160.4.a.a 1 1
2160.4.a.b 1
2160.4.a.c 1
2160.4.a.d 1
2160.4.a.e 1
2160.4.a.f 1
2160.4.a.g 1
2160.4.a.h 1
2160.4.a.i 1
2160.4.a.j 1
2160.4.a.k 1
2160.4.a.l 1
2160.4.a.m 1
2160.4.a.n 1
2160.4.a.o 1
2160.4.a.p 1
2160.4.a.q 1
2160.4.a.r 1
2160.4.a.s 1
2160.4.a.t 1
2160.4.a.u 2
2160.4.a.v 2
2160.4.a.w 2
2160.4.a.x 2
2160.4.a.y 2
2160.4.a.z 2
2160.4.a.ba 2
2160.4.a.bb 2
2160.4.a.bc 2
2160.4.a.bd 2
2160.4.a.be 3
2160.4.a.bf 3
2160.4.a.bg 3
2160.4.a.bh 3
2160.4.a.bi 3
2160.4.a.bj 3
2160.4.a.bk 3
2160.4.a.bl 3
2160.4.a.bm 3
2160.4.a.bn 3
2160.4.a.bo 3
2160.4.a.bp 3
2160.4.a.bq 3
2160.4.a.br 3
2160.4.a.bs 3
2160.4.a.bt 3
2160.4.a.bu 4
2160.4.a.bv 4
2160.4.b \(\chi_{2160}(1511, \cdot)\) None 0 1
2160.4.d \(\chi_{2160}(649, \cdot)\) None 0 1
2160.4.f \(\chi_{2160}(1729, \cdot)\) n/a 144 1
2160.4.h \(\chi_{2160}(431, \cdot)\) 2160.4.h.a 4 1
2160.4.h.b 4
2160.4.h.c 12
2160.4.h.d 12
2160.4.h.e 12
2160.4.h.f 16
2160.4.h.g 16
2160.4.h.h 20
2160.4.k \(\chi_{2160}(1081, \cdot)\) None 0 1
2160.4.m \(\chi_{2160}(1079, \cdot)\) None 0 1
2160.4.o \(\chi_{2160}(2159, \cdot)\) n/a 144 1
2160.4.q \(\chi_{2160}(721, \cdot)\) n/a 144 2
2160.4.t \(\chi_{2160}(541, \cdot)\) n/a 768 2
2160.4.u \(\chi_{2160}(539, \cdot)\) n/a 1152 2
2160.4.w \(\chi_{2160}(593, \cdot)\) n/a 288 2
2160.4.x \(\chi_{2160}(703, \cdot)\) n/a 288 2
2160.4.z \(\chi_{2160}(163, \cdot)\) n/a 1152 2
2160.4.bc \(\chi_{2160}(917, \cdot)\) n/a 1152 2
2160.4.bd \(\chi_{2160}(1027, \cdot)\) n/a 1152 2
2160.4.bg \(\chi_{2160}(53, \cdot)\) n/a 1152 2
2160.4.bi \(\chi_{2160}(487, \cdot)\) None 0 2
2160.4.bj \(\chi_{2160}(377, \cdot)\) None 0 2
2160.4.bl \(\chi_{2160}(971, \cdot)\) n/a 768 2
2160.4.bm \(\chi_{2160}(109, \cdot)\) n/a 1152 2
2160.4.br \(\chi_{2160}(719, \cdot)\) n/a 216 2
2160.4.bt \(\chi_{2160}(359, \cdot)\) None 0 2
2160.4.bv \(\chi_{2160}(361, \cdot)\) None 0 2
2160.4.bw \(\chi_{2160}(1151, \cdot)\) n/a 144 2
2160.4.by \(\chi_{2160}(289, \cdot)\) n/a 212 2
2160.4.ca \(\chi_{2160}(1369, \cdot)\) None 0 2
2160.4.cc \(\chi_{2160}(71, \cdot)\) None 0 2
2160.4.ce \(\chi_{2160}(241, \cdot)\) n/a 1296 6
2160.4.cf \(\chi_{2160}(469, \cdot)\) n/a 1712 4
2160.4.cg \(\chi_{2160}(251, \cdot)\) n/a 1152 4
2160.4.cj \(\chi_{2160}(343, \cdot)\) None 0 4
2160.4.cm \(\chi_{2160}(233, \cdot)\) None 0 4
2160.4.cn \(\chi_{2160}(557, \cdot)\) n/a 1712 4
2160.4.cq \(\chi_{2160}(307, \cdot)\) n/a 1712 4
2160.4.cr \(\chi_{2160}(197, \cdot)\) n/a 1712 4
2160.4.cu \(\chi_{2160}(667, \cdot)\) n/a 1712 4
2160.4.cv \(\chi_{2160}(17, \cdot)\) n/a 424 4
2160.4.cy \(\chi_{2160}(127, \cdot)\) n/a 432 4
2160.4.db \(\chi_{2160}(179, \cdot)\) n/a 1712 4
2160.4.dc \(\chi_{2160}(181, \cdot)\) n/a 1152 4
2160.4.dd \(\chi_{2160}(119, \cdot)\) None 0 6
2160.4.di \(\chi_{2160}(121, \cdot)\) None 0 6
2160.4.dj \(\chi_{2160}(239, \cdot)\) n/a 1944 6
2160.4.dm \(\chi_{2160}(49, \cdot)\) n/a 1932 6
2160.4.dn \(\chi_{2160}(311, \cdot)\) None 0 6
2160.4.do \(\chi_{2160}(191, \cdot)\) n/a 1296 6
2160.4.dp \(\chi_{2160}(169, \cdot)\) None 0 6
2160.4.du \(\chi_{2160}(59, \cdot)\) n/a 15504 12
2160.4.dv \(\chi_{2160}(61, \cdot)\) n/a 10368 12
2160.4.dy \(\chi_{2160}(137, \cdot)\) None 0 12
2160.4.dz \(\chi_{2160}(223, \cdot)\) n/a 3888 12
2160.4.ea \(\chi_{2160}(43, \cdot)\) n/a 15504 12
2160.4.ec \(\chi_{2160}(77, \cdot)\) n/a 15504 12
2160.4.ee \(\chi_{2160}(173, \cdot)\) n/a 15504 12
2160.4.eg \(\chi_{2160}(187, \cdot)\) n/a 15504 12
2160.4.ek \(\chi_{2160}(113, \cdot)\) n/a 3864 12
2160.4.el \(\chi_{2160}(7, \cdot)\) None 0 12
2160.4.eo \(\chi_{2160}(229, \cdot)\) n/a 15504 12
2160.4.ep \(\chi_{2160}(11, \cdot)\) n/a 10368 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2160))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2160)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2160))\)\(^{\oplus 1}\)