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Properties

Label 2160.3
Level 2160
Weight 3
Dimension 100944
Nonzero newspaces 42
Sturm bound 746496
Trace bound 31

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Defining parameters

Level: \( N \) = \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(746496\)
Trace bound: \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2160))\).

Total New Old
Modular forms 252192 101808 150384
Cusp forms 245472 100944 144528
Eisenstein series 6720 864 5856

Trace form

\( 100944 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 61 q^{5} - 144 q^{6} - 58 q^{7} - 32 q^{8} - 12 q^{9} + O(q^{10}) \) \( 100944 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 61 q^{5} - 144 q^{6} - 58 q^{7} - 32 q^{8} - 12 q^{9} - 84 q^{10} - 70 q^{11} - 48 q^{12} - 54 q^{13} - 54 q^{15} - 56 q^{16} + 82 q^{17} - 48 q^{18} + 22 q^{19} + 36 q^{20} - 180 q^{21} - 8 q^{22} - 14 q^{23} - 48 q^{24} - 53 q^{25} - 288 q^{26} + 252 q^{27} - 368 q^{28} + 250 q^{29} - 72 q^{30} - 14 q^{31} - 392 q^{32} - 12 q^{33} - 232 q^{34} + 59 q^{35} - 144 q^{36} - 118 q^{37} - 536 q^{38} - 324 q^{39} - 308 q^{40} - 458 q^{41} - 48 q^{42} - 74 q^{43} - 296 q^{44} - 330 q^{45} - 296 q^{46} - 606 q^{47} - 48 q^{48} - 64 q^{49} + 92 q^{50} - 162 q^{51} + 264 q^{52} - 48 q^{53} - 48 q^{54} - 370 q^{55} - 1336 q^{56} - 738 q^{57} - 1016 q^{58} - 1466 q^{59} - 1392 q^{60} - 1634 q^{61} - 3664 q^{62} - 516 q^{63} - 1064 q^{64} - 1357 q^{65} - 1944 q^{66} - 554 q^{67} - 1464 q^{68} - 444 q^{69} - 276 q^{70} - 698 q^{71} + 288 q^{72} - 206 q^{73} + 1648 q^{74} + 114 q^{75} + 1752 q^{76} + 1882 q^{77} + 2136 q^{78} - 26 q^{79} + 2172 q^{80} + 1596 q^{81} + 416 q^{82} + 458 q^{83} + 3384 q^{84} + 1113 q^{85} + 4968 q^{86} + 540 q^{87} + 1560 q^{88} + 1134 q^{89} + 900 q^{90} + 134 q^{91} - 616 q^{92} - 2076 q^{93} - 88 q^{94} - 637 q^{95} - 144 q^{96} + 546 q^{97} + 16 q^{98} - 1764 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2160))\)

We only show spaces with odd 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
2160.3.c \(\chi_{2160}(1889, \cdot)\) 2160.3.c.a 2 1
2160.3.c.b 2
2160.3.c.c 2
2160.3.c.d 2
2160.3.c.e 2
2160.3.c.f 2
2160.3.c.g 4
2160.3.c.h 4
2160.3.c.i 4
2160.3.c.j 4
2160.3.c.k 4
2160.3.c.l 4
2160.3.c.m 4
2160.3.c.n 8
2160.3.c.o 12
2160.3.c.p 12
2160.3.c.q 24
2160.3.e \(\chi_{2160}(271, \cdot)\) 2160.3.e.a 4 1
2160.3.e.b 4
2160.3.e.c 8
2160.3.e.d 12
2160.3.e.e 12
2160.3.e.f 12
2160.3.e.g 12
2160.3.g \(\chi_{2160}(1351, \cdot)\) None 0 1
2160.3.i \(\chi_{2160}(809, \cdot)\) None 0 1
2160.3.j \(\chi_{2160}(1999, \cdot)\) 2160.3.j.a 16 1
2160.3.j.b 16
2160.3.j.c 32
2160.3.j.d 32
2160.3.l \(\chi_{2160}(161, \cdot)\) 2160.3.l.a 2 1
2160.3.l.b 2
2160.3.l.c 2
2160.3.l.d 2
2160.3.l.e 4
2160.3.l.f 4
2160.3.l.g 4
2160.3.l.h 4
2160.3.l.i 8
2160.3.l.j 8
2160.3.l.k 8
2160.3.l.l 16
2160.3.n \(\chi_{2160}(1241, \cdot)\) None 0 1
2160.3.p \(\chi_{2160}(919, \cdot)\) None 0 1
2160.3.r \(\chi_{2160}(379, \cdot)\) n/a 768 2
2160.3.s \(\chi_{2160}(701, \cdot)\) n/a 512 2
2160.3.v \(\chi_{2160}(647, \cdot)\) None 0 2
2160.3.y \(\chi_{2160}(217, \cdot)\) None 0 2
2160.3.ba \(\chi_{2160}(107, \cdot)\) n/a 768 2
2160.3.bb \(\chi_{2160}(757, \cdot)\) n/a 768 2
2160.3.be \(\chi_{2160}(1187, \cdot)\) n/a 768 2
2160.3.bf \(\chi_{2160}(1837, \cdot)\) n/a 768 2
2160.3.bh \(\chi_{2160}(433, \cdot)\) n/a 192 2
2160.3.bk \(\chi_{2160}(863, \cdot)\) n/a 192 2
2160.3.bn \(\chi_{2160}(269, \cdot)\) n/a 768 2
2160.3.bo \(\chi_{2160}(811, \cdot)\) n/a 512 2
2160.3.bp \(\chi_{2160}(199, \cdot)\) None 0 2
2160.3.bq \(\chi_{2160}(521, \cdot)\) None 0 2
2160.3.bs \(\chi_{2160}(881, \cdot)\) 2160.3.bs.a 4 2
2160.3.bs.b 12
2160.3.bs.c 16
2160.3.bs.d 16
2160.3.bs.e 48
2160.3.bu \(\chi_{2160}(559, \cdot)\) n/a 144 2
2160.3.bx \(\chi_{2160}(89, \cdot)\) None 0 2
2160.3.bz \(\chi_{2160}(631, \cdot)\) None 0 2
2160.3.cb \(\chi_{2160}(991, \cdot)\) 2160.3.cb.a 32 2
2160.3.cb.b 32
2160.3.cb.c 32
2160.3.cd \(\chi_{2160}(449, \cdot)\) n/a 140 2
2160.3.ch \(\chi_{2160}(91, \cdot)\) n/a 768 4
2160.3.ci \(\chi_{2160}(629, \cdot)\) n/a 1136 4
2160.3.ck \(\chi_{2160}(577, \cdot)\) n/a 280 4
2160.3.cl \(\chi_{2160}(143, \cdot)\) n/a 288 4
2160.3.co \(\chi_{2160}(397, \cdot)\) n/a 1136 4
2160.3.cp \(\chi_{2160}(467, \cdot)\) n/a 1136 4
2160.3.cs \(\chi_{2160}(37, \cdot)\) n/a 1136 4
2160.3.ct \(\chi_{2160}(827, \cdot)\) n/a 1136 4
2160.3.cw \(\chi_{2160}(503, \cdot)\) None 0 4
2160.3.cx \(\chi_{2160}(73, \cdot)\) None 0 4
2160.3.cz \(\chi_{2160}(341, \cdot)\) n/a 768 4
2160.3.da \(\chi_{2160}(19, \cdot)\) n/a 1136 4
2160.3.de \(\chi_{2160}(151, \cdot)\) None 0 6
2160.3.df \(\chi_{2160}(209, \cdot)\) n/a 1284 6
2160.3.dg \(\chi_{2160}(329, \cdot)\) None 0 6
2160.3.dh \(\chi_{2160}(31, \cdot)\) n/a 864 6
2160.3.dk \(\chi_{2160}(401, \cdot)\) n/a 864 6
2160.3.dl \(\chi_{2160}(439, \cdot)\) None 0 6
2160.3.dq \(\chi_{2160}(79, \cdot)\) n/a 1296 6
2160.3.dr \(\chi_{2160}(41, \cdot)\) None 0 6
2160.3.ds \(\chi_{2160}(29, \cdot)\) n/a 10320 12
2160.3.dt \(\chi_{2160}(211, \cdot)\) n/a 6912 12
2160.3.dw \(\chi_{2160}(47, \cdot)\) n/a 2592 12
2160.3.dx \(\chi_{2160}(313, \cdot)\) None 0 12
2160.3.eb \(\chi_{2160}(133, \cdot)\) n/a 10320 12
2160.3.ed \(\chi_{2160}(203, \cdot)\) n/a 10320 12
2160.3.ef \(\chi_{2160}(83, \cdot)\) n/a 10320 12
2160.3.eh \(\chi_{2160}(13, \cdot)\) n/a 10320 12
2160.3.ei \(\chi_{2160}(23, \cdot)\) None 0 12
2160.3.ej \(\chi_{2160}(97, \cdot)\) n/a 2568 12
2160.3.em \(\chi_{2160}(139, \cdot)\) n/a 10320 12
2160.3.en \(\chi_{2160}(101, \cdot)\) n/a 6912 12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2160))\) into lower level spaces

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