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Properties

Label 1440.3
Level 1440
Weight 3
Dimension 44874
Nonzero newspaces 40
Sturm bound 331776
Trace bound 53

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Defining parameters

Level: \( N \) = \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(331776\)
Trace bound: \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1440))\).

Total New Old
Modular forms 112640 45414 67226
Cusp forms 108544 44874 63670
Eisenstein series 4096 540 3556

Trace form

\( 44874 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 40 q^{5} - 96 q^{6} - 16 q^{7} - 24 q^{8} - 48 q^{9} + O(q^{10}) \) \( 44874 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 40 q^{5} - 96 q^{6} - 16 q^{7} - 24 q^{8} - 48 q^{9} - 68 q^{10} - 16 q^{11} - 32 q^{12} + 32 q^{13} + 8 q^{14} - 18 q^{15} - 112 q^{16} + 100 q^{17} - 32 q^{18} + 12 q^{19} - 116 q^{20} - 32 q^{21} - 320 q^{22} + 104 q^{23} - 32 q^{24} - 78 q^{25} - 272 q^{26} - 120 q^{27} - 192 q^{28} - 272 q^{29} - 80 q^{30} - 188 q^{31} + 16 q^{32} - 312 q^{33} + 64 q^{34} - 228 q^{35} - 624 q^{36} - 512 q^{37} - 1256 q^{38} - 252 q^{39} - 528 q^{40} - 796 q^{41} - 832 q^{42} - 564 q^{43} - 712 q^{44} - 144 q^{45} - 408 q^{46} - 240 q^{47} + 176 q^{48} - 118 q^{49} + 276 q^{50} + 16 q^{51} + 408 q^{52} + 1072 q^{53} + 1200 q^{54} - 80 q^{55} + 1696 q^{56} + 144 q^{57} + 1728 q^{58} - 152 q^{59} + 680 q^{60} + 944 q^{61} + 1104 q^{62} - 468 q^{63} - 336 q^{64} - 476 q^{65} - 96 q^{66} + 268 q^{67} - 16 q^{68} - 288 q^{69} - 672 q^{70} + 208 q^{71} - 32 q^{72} - 668 q^{73} + 152 q^{74} + 206 q^{75} + 568 q^{76} - 152 q^{77} + 784 q^{78} - 1820 q^{79} + 1728 q^{80} + 784 q^{81} + 3288 q^{82} - 2892 q^{83} + 2432 q^{84} + 144 q^{85} + 3184 q^{86} - 1532 q^{87} + 2448 q^{88} - 52 q^{89} + 672 q^{90} - 1704 q^{91} + 2432 q^{92} - 32 q^{93} + 1824 q^{94} + 216 q^{95} - 368 q^{96} + 1012 q^{97} + 32 q^{98} + 932 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1440))\)

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
1440.3.c \(\chi_{1440}(449, \cdot)\) 1440.3.c.a 4 1
1440.3.c.b 4
1440.3.c.c 16
1440.3.c.d 24
1440.3.e \(\chi_{1440}(991, \cdot)\) 1440.3.e.a 4 1
1440.3.e.b 4
1440.3.e.c 8
1440.3.e.d 8
1440.3.e.e 8
1440.3.e.f 8
1440.3.g \(\chi_{1440}(271, \cdot)\) 1440.3.g.a 8 1
1440.3.g.b 16
1440.3.g.c 16
1440.3.i \(\chi_{1440}(1169, \cdot)\) 1440.3.i.a 48 1
1440.3.j \(\chi_{1440}(1279, \cdot)\) 1440.3.j.a 6 1
1440.3.j.b 6
1440.3.j.c 12
1440.3.j.d 12
1440.3.j.e 12
1440.3.j.f 12
1440.3.l \(\chi_{1440}(161, \cdot)\) 1440.3.l.a 8 1
1440.3.l.b 8
1440.3.l.c 8
1440.3.l.d 8
1440.3.n \(\chi_{1440}(881, \cdot)\) 1440.3.n.a 32 1
1440.3.p \(\chi_{1440}(559, \cdot)\) 1440.3.p.a 1 1
1440.3.p.b 1
1440.3.p.c 2
1440.3.p.d 2
1440.3.p.e 2
1440.3.p.f 2
1440.3.p.g 8
1440.3.p.h 16
1440.3.p.i 24
1440.3.r \(\chi_{1440}(199, \cdot)\) None 0 2
1440.3.s \(\chi_{1440}(521, \cdot)\) None 0 2
1440.3.v \(\chi_{1440}(143, \cdot)\) 1440.3.v.a 96 2
1440.3.y \(\chi_{1440}(433, \cdot)\) n/a 116 2
1440.3.ba \(\chi_{1440}(503, \cdot)\) None 0 2
1440.3.bb \(\chi_{1440}(73, \cdot)\) None 0 2
1440.3.be \(\chi_{1440}(1223, \cdot)\) None 0 2
1440.3.bf \(\chi_{1440}(793, \cdot)\) None 0 2
1440.3.bh \(\chi_{1440}(577, \cdot)\) n/a 120 2
1440.3.bk \(\chi_{1440}(287, \cdot)\) 1440.3.bk.a 4 2
1440.3.bk.b 4
1440.3.bk.c 4
1440.3.bk.d 4
1440.3.bk.e 20
1440.3.bk.f 20
1440.3.bk.g 20
1440.3.bk.h 20
1440.3.bn \(\chi_{1440}(89, \cdot)\) None 0 2
1440.3.bo \(\chi_{1440}(631, \cdot)\) None 0 2
1440.3.bp \(\chi_{1440}(79, \cdot)\) n/a 280 2
1440.3.bq \(\chi_{1440}(401, \cdot)\) n/a 192 2
1440.3.bs \(\chi_{1440}(641, \cdot)\) n/a 192 2
1440.3.bu \(\chi_{1440}(319, \cdot)\) n/a 288 2
1440.3.bx \(\chi_{1440}(209, \cdot)\) n/a 280 2
1440.3.bz \(\chi_{1440}(751, \cdot)\) n/a 192 2
1440.3.cb \(\chi_{1440}(31, \cdot)\) n/a 192 2
1440.3.cd \(\chi_{1440}(929, \cdot)\) n/a 288 2
1440.3.cf \(\chi_{1440}(37, \cdot)\) n/a 952 4
1440.3.cg \(\chi_{1440}(467, \cdot)\) n/a 768 4
1440.3.cj \(\chi_{1440}(91, \cdot)\) n/a 640 4
1440.3.ck \(\chi_{1440}(269, \cdot)\) n/a 768 4
1440.3.cm \(\chi_{1440}(19, \cdot)\) n/a 952 4
1440.3.cp \(\chi_{1440}(341, \cdot)\) n/a 512 4
1440.3.cq \(\chi_{1440}(107, \cdot)\) n/a 768 4
1440.3.ct \(\chi_{1440}(397, \cdot)\) n/a 952 4
1440.3.cw \(\chi_{1440}(151, \cdot)\) None 0 4
1440.3.cx \(\chi_{1440}(329, \cdot)\) None 0 4
1440.3.cz \(\chi_{1440}(97, \cdot)\) n/a 576 4
1440.3.da \(\chi_{1440}(383, \cdot)\) n/a 576 4
1440.3.dd \(\chi_{1440}(313, \cdot)\) None 0 4
1440.3.de \(\chi_{1440}(263, \cdot)\) None 0 4
1440.3.dh \(\chi_{1440}(553, \cdot)\) None 0 4
1440.3.di \(\chi_{1440}(23, \cdot)\) None 0 4
1440.3.dl \(\chi_{1440}(47, \cdot)\) n/a 560 4
1440.3.dm \(\chi_{1440}(337, \cdot)\) n/a 560 4
1440.3.do \(\chi_{1440}(41, \cdot)\) None 0 4
1440.3.dp \(\chi_{1440}(439, \cdot)\) None 0 4
1440.3.ds \(\chi_{1440}(133, \cdot)\) n/a 4576 8
1440.3.dv \(\chi_{1440}(83, \cdot)\) n/a 4576 8
1440.3.dx \(\chi_{1440}(29, \cdot)\) n/a 4576 8
1440.3.dy \(\chi_{1440}(211, \cdot)\) n/a 3072 8
1440.3.ea \(\chi_{1440}(101, \cdot)\) n/a 3072 8
1440.3.ed \(\chi_{1440}(139, \cdot)\) n/a 4576 8
1440.3.ef \(\chi_{1440}(203, \cdot)\) n/a 4576 8
1440.3.eg \(\chi_{1440}(13, \cdot)\) n/a 4576 8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1440))\) into lower level spaces

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