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Properties

Label 2880.3
Level 2880
Weight 3
Dimension 179982
Nonzero newspaces 56
Sturm bound 1327104
Trace bound 81

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Defining parameters

Level: \( N \) = \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(1327104\)
Trace bound: \(81\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2880))\).

Total New Old
Modular forms 446976 181170 265806
Cusp forms 437760 179982 257778
Eisenstein series 9216 1188 8028

Trace form

\( 179982 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 72 q^{5} - 192 q^{6} - 40 q^{7} - 48 q^{8} - 80 q^{9} + O(q^{10}) \) \( 179982 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 72 q^{5} - 192 q^{6} - 40 q^{7} - 48 q^{8} - 80 q^{9} - 216 q^{10} - 140 q^{11} - 64 q^{12} - 80 q^{13} - 48 q^{14} - 72 q^{15} - 144 q^{16} - 52 q^{17} - 64 q^{18} - 44 q^{19} - 72 q^{20} - 192 q^{21} + 96 q^{22} + 104 q^{23} - 64 q^{24} + 6 q^{25} + 256 q^{26} - 48 q^{27} + 96 q^{28} + 16 q^{29} - 96 q^{30} - 88 q^{31} - 128 q^{32} + 24 q^{33} - 288 q^{34} + 48 q^{35} - 192 q^{36} + 144 q^{37} - 608 q^{38} + 336 q^{39} - 432 q^{40} + 76 q^{41} - 64 q^{42} + 252 q^{43} - 256 q^{44} - 432 q^{46} - 48 q^{47} - 64 q^{48} - 178 q^{49} - 384 q^{50} - 464 q^{51} - 1104 q^{52} - 912 q^{53} - 64 q^{54} + 92 q^{55} - 928 q^{56} - 720 q^{57} - 768 q^{58} - 260 q^{59} - 96 q^{60} - 816 q^{61} - 336 q^{62} - 440 q^{63} + 48 q^{64} - 44 q^{65} - 192 q^{66} - 548 q^{67} + 432 q^{68} - 208 q^{69} + 600 q^{70} - 1144 q^{71} - 64 q^{72} - 308 q^{73} + 1184 q^{74} - 108 q^{75} + 1520 q^{76} - 1128 q^{77} - 1696 q^{78} - 2088 q^{79} - 2544 q^{80} - 2128 q^{81} - 6384 q^{82} - 1636 q^{83} - 4992 q^{84} - 1464 q^{85} - 5760 q^{86} - 944 q^{87} - 3408 q^{88} - 2684 q^{89} - 1536 q^{90} - 1480 q^{91} - 2784 q^{92} - 448 q^{93} - 624 q^{94} - 852 q^{95} + 352 q^{96} - 4 q^{97} + 2400 q^{98} + 464 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2880))\)

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
2880.3.c \(\chi_{2880}(449, \cdot)\) 2880.3.c.a 4 1
2880.3.c.b 4
2880.3.c.c 4
2880.3.c.d 4
2880.3.c.e 4
2880.3.c.f 4
2880.3.c.g 4
2880.3.c.h 4
2880.3.c.i 12
2880.3.c.j 12
2880.3.c.k 16
2880.3.c.l 24
2880.3.e \(\chi_{2880}(2431, \cdot)\) 2880.3.e.a 4 1
2880.3.e.b 4
2880.3.e.c 4
2880.3.e.d 4
2880.3.e.e 4
2880.3.e.f 4
2880.3.e.g 4
2880.3.e.h 4
2880.3.e.i 8
2880.3.e.j 8
2880.3.e.k 8
2880.3.e.l 8
2880.3.e.m 8
2880.3.e.n 8
2880.3.g \(\chi_{2880}(991, \cdot)\) 2880.3.g.a 8 1
2880.3.g.b 8
2880.3.g.c 8
2880.3.g.d 8
2880.3.g.e 8
2880.3.g.f 8
2880.3.g.g 16
2880.3.g.h 16
2880.3.i \(\chi_{2880}(1889, \cdot)\) 2880.3.i.a 8 1
2880.3.i.b 8
2880.3.i.c 16
2880.3.i.d 64
2880.3.j \(\chi_{2880}(1279, \cdot)\) n/a 118 1
2880.3.l \(\chi_{2880}(1601, \cdot)\) 2880.3.l.a 4 1
2880.3.l.b 4
2880.3.l.c 4
2880.3.l.d 4
2880.3.l.e 4
2880.3.l.f 4
2880.3.l.g 4
2880.3.l.h 4
2880.3.l.i 8
2880.3.l.j 8
2880.3.l.k 8
2880.3.l.l 8
2880.3.n \(\chi_{2880}(161, \cdot)\) 2880.3.n.a 16 1
2880.3.n.b 48
2880.3.p \(\chi_{2880}(2719, \cdot)\) n/a 120 1
2880.3.r \(\chi_{2880}(559, \cdot)\) n/a 236 2
2880.3.s \(\chi_{2880}(881, \cdot)\) n/a 128 2
2880.3.v \(\chi_{2880}(287, \cdot)\) n/a 192 2
2880.3.y \(\chi_{2880}(2017, \cdot)\) n/a 240 2
2880.3.ba \(\chi_{2880}(1583, \cdot)\) n/a 192 2
2880.3.bb \(\chi_{2880}(1873, \cdot)\) n/a 236 2
2880.3.be \(\chi_{2880}(143, \cdot)\) n/a 192 2
2880.3.bf \(\chi_{2880}(433, \cdot)\) n/a 236 2
2880.3.bh \(\chi_{2880}(577, \cdot)\) n/a 236 2
2880.3.bk \(\chi_{2880}(1727, \cdot)\) n/a 192 2
2880.3.bn \(\chi_{2880}(1169, \cdot)\) n/a 192 2
2880.3.bo \(\chi_{2880}(271, \cdot)\) n/a 160 2
2880.3.bp \(\chi_{2880}(799, \cdot)\) n/a 576 2
2880.3.bq \(\chi_{2880}(1121, \cdot)\) n/a 384 2
2880.3.bs \(\chi_{2880}(641, \cdot)\) n/a 384 2
2880.3.bu \(\chi_{2880}(319, \cdot)\) n/a 568 2
2880.3.bx \(\chi_{2880}(929, \cdot)\) n/a 576 2
2880.3.bz \(\chi_{2880}(31, \cdot)\) n/a 384 2
2880.3.cb \(\chi_{2880}(511, \cdot)\) n/a 384 2
2880.3.cd \(\chi_{2880}(1409, \cdot)\) n/a 568 2
2880.3.cf \(\chi_{2880}(73, \cdot)\) None 0 4
2880.3.cg \(\chi_{2880}(1223, \cdot)\) None 0 4
2880.3.cj \(\chi_{2880}(631, \cdot)\) None 0 4
2880.3.ck \(\chi_{2880}(89, \cdot)\) None 0 4
2880.3.cm \(\chi_{2880}(199, \cdot)\) None 0 4
2880.3.cp \(\chi_{2880}(521, \cdot)\) None 0 4
2880.3.cq \(\chi_{2880}(503, \cdot)\) None 0 4
2880.3.ct \(\chi_{2880}(793, \cdot)\) None 0 4
2880.3.cw \(\chi_{2880}(751, \cdot)\) n/a 768 4
2880.3.cx \(\chi_{2880}(209, \cdot)\) n/a 1136 4
2880.3.cz \(\chi_{2880}(193, \cdot)\) n/a 1136 4
2880.3.da \(\chi_{2880}(383, \cdot)\) n/a 1136 4
2880.3.dd \(\chi_{2880}(337, \cdot)\) n/a 1136 4
2880.3.de \(\chi_{2880}(47, \cdot)\) n/a 1136 4
2880.3.dh \(\chi_{2880}(817, \cdot)\) n/a 1136 4
2880.3.di \(\chi_{2880}(527, \cdot)\) n/a 1136 4
2880.3.dl \(\chi_{2880}(1247, \cdot)\) n/a 1152 4
2880.3.dm \(\chi_{2880}(97, \cdot)\) n/a 1152 4
2880.3.do \(\chi_{2880}(401, \cdot)\) n/a 768 4
2880.3.dp \(\chi_{2880}(79, \cdot)\) n/a 1136 4
2880.3.ds \(\chi_{2880}(397, \cdot)\) n/a 3824 8
2880.3.dv \(\chi_{2880}(107, \cdot)\) n/a 3072 8
2880.3.dx \(\chi_{2880}(341, \cdot)\) n/a 2048 8
2880.3.dz \(\chi_{2880}(269, \cdot)\) n/a 3072 8
2880.3.ea \(\chi_{2880}(91, \cdot)\) n/a 2560 8
2880.3.ec \(\chi_{2880}(19, \cdot)\) n/a 3824 8
2880.3.ee \(\chi_{2880}(37, \cdot)\) n/a 3824 8
2880.3.eh \(\chi_{2880}(467, \cdot)\) n/a 3072 8
2880.3.ei \(\chi_{2880}(313, \cdot)\) None 0 8
2880.3.el \(\chi_{2880}(23, \cdot)\) None 0 8
2880.3.en \(\chi_{2880}(329, \cdot)\) None 0 8
2880.3.eo \(\chi_{2880}(151, \cdot)\) None 0 8
2880.3.eq \(\chi_{2880}(41, \cdot)\) None 0 8
2880.3.et \(\chi_{2880}(439, \cdot)\) None 0 8
2880.3.ev \(\chi_{2880}(263, \cdot)\) None 0 8
2880.3.ew \(\chi_{2880}(553, \cdot)\) None 0 8
2880.3.ez \(\chi_{2880}(83, \cdot)\) n/a 18368 16
2880.3.fa \(\chi_{2880}(133, \cdot)\) n/a 18368 16
2880.3.fc \(\chi_{2880}(139, \cdot)\) n/a 18368 16
2880.3.fe \(\chi_{2880}(211, \cdot)\) n/a 12288 16
2880.3.fh \(\chi_{2880}(29, \cdot)\) n/a 18368 16
2880.3.fj \(\chi_{2880}(101, \cdot)\) n/a 12288 16
2880.3.fl \(\chi_{2880}(203, \cdot)\) n/a 18368 16
2880.3.fm \(\chi_{2880}(13, \cdot)\) n/a 18368 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2880))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2880)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 2}\)