Properties

Label 3024.2
Level 3024
Weight 2
Dimension 105264
Nonzero newspaces 64
Sturm bound 995328
Trace bound 45

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Defining parameters

Level: \( N \) = \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(995328\)
Trace bound: \(45\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3024))\).

Total New Old
Modular forms 253872 106704 147168
Cusp forms 243793 105264 138529
Eisenstein series 10079 1440 8639

Trace form

\( 105264 q - 64 q^{2} - 72 q^{3} - 112 q^{4} - 78 q^{5} - 96 q^{6} - 103 q^{7} - 160 q^{8} - 24 q^{9} + O(q^{10}) \) \( 105264 q - 64 q^{2} - 72 q^{3} - 112 q^{4} - 78 q^{5} - 96 q^{6} - 103 q^{7} - 160 q^{8} - 24 q^{9} - 112 q^{10} - 38 q^{11} - 96 q^{12} - 132 q^{13} - 88 q^{14} - 180 q^{15} - 128 q^{16} - 162 q^{17} - 96 q^{18} - 88 q^{19} - 120 q^{20} - 150 q^{21} - 328 q^{22} - 70 q^{23} - 96 q^{24} - 70 q^{25} - 128 q^{26} - 108 q^{27} - 344 q^{28} - 310 q^{29} - 96 q^{30} - 136 q^{31} - 104 q^{32} - 264 q^{33} - 128 q^{34} - 145 q^{35} - 240 q^{36} - 212 q^{37} - 8 q^{38} - 144 q^{39} - 48 q^{40} - 108 q^{41} - 120 q^{42} - 334 q^{43} + 24 q^{44} - 168 q^{45} - 16 q^{46} - 190 q^{47} - 96 q^{48} - 307 q^{49} - 72 q^{50} - 54 q^{51} - 48 q^{52} - 72 q^{53} - 96 q^{54} - 228 q^{55} + 100 q^{56} - 30 q^{57} + 80 q^{58} - 14 q^{59} + 144 q^{60} - 4 q^{61} + 416 q^{62} - 60 q^{63} - 136 q^{64} + 200 q^{65} + 264 q^{66} - 4 q^{67} + 488 q^{68} + 72 q^{69} + 52 q^{70} + 46 q^{71} + 240 q^{72} + 52 q^{73} + 496 q^{74} + 12 q^{75} + 272 q^{76} - 33 q^{77} + 72 q^{78} - 52 q^{79} + 600 q^{80} - 24 q^{81} - 32 q^{82} + 44 q^{83} + 12 q^{84} - 354 q^{85} + 440 q^{86} - 36 q^{87} + 96 q^{88} + 6 q^{89} + 120 q^{90} - 129 q^{91} - 40 q^{92} + 24 q^{93} - 48 q^{94} + 166 q^{95} - 96 q^{96} - 348 q^{97} - 4 q^{98} + 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3024))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3024.2.a \(\chi_{3024}(1, \cdot)\) 3024.2.a.a 1 1
3024.2.a.b 1
3024.2.a.c 1
3024.2.a.d 1
3024.2.a.e 1
3024.2.a.f 1
3024.2.a.g 1
3024.2.a.h 1
3024.2.a.i 1
3024.2.a.j 1
3024.2.a.k 1
3024.2.a.l 1
3024.2.a.m 1
3024.2.a.n 1
3024.2.a.o 1
3024.2.a.p 1
3024.2.a.q 1
3024.2.a.r 1
3024.2.a.s 1
3024.2.a.t 1
3024.2.a.u 1
3024.2.a.v 1
3024.2.a.w 1
3024.2.a.x 1
3024.2.a.y 1
3024.2.a.z 1
3024.2.a.ba 1
3024.2.a.bb 1
3024.2.a.bc 1
3024.2.a.bd 1
3024.2.a.be 2
3024.2.a.bf 2
3024.2.a.bg 2
3024.2.a.bh 2
3024.2.a.bi 2
3024.2.a.bj 2
3024.2.a.bk 2
3024.2.a.bl 2
3024.2.a.bm 2
3024.2.b \(\chi_{3024}(1567, \cdot)\) 3024.2.b.a 2 1
3024.2.b.b 2
3024.2.b.c 2
3024.2.b.d 2
3024.2.b.e 2
3024.2.b.f 2
3024.2.b.g 2
3024.2.b.h 2
3024.2.b.i 2
3024.2.b.j 2
3024.2.b.k 2
3024.2.b.l 2
3024.2.b.m 2
3024.2.b.n 2
3024.2.b.o 2
3024.2.b.p 2
3024.2.b.q 4
3024.2.b.r 4
3024.2.b.s 4
3024.2.b.t 4
3024.2.b.u 8
3024.2.b.v 8
3024.2.c \(\chi_{3024}(1513, \cdot)\) None 0 1
3024.2.h \(\chi_{3024}(2591, \cdot)\) 3024.2.h.a 8 1
3024.2.h.b 8
3024.2.h.c 8
3024.2.h.d 8
3024.2.h.e 8
3024.2.h.f 8
3024.2.i \(\chi_{3024}(377, \cdot)\) None 0 1
3024.2.j \(\chi_{3024}(1079, \cdot)\) None 0 1
3024.2.k \(\chi_{3024}(1889, \cdot)\) 3024.2.k.a 2 1
3024.2.k.b 2
3024.2.k.c 2
3024.2.k.d 2
3024.2.k.e 4
3024.2.k.f 4
3024.2.k.g 4
3024.2.k.h 4
3024.2.k.i 4
3024.2.k.j 4
3024.2.k.k 16
3024.2.k.l 16
3024.2.p \(\chi_{3024}(55, \cdot)\) None 0 1
3024.2.q \(\chi_{3024}(2305, \cdot)\) 3024.2.q.a 2 2
3024.2.q.b 2
3024.2.q.c 2
3024.2.q.d 2
3024.2.q.e 2
3024.2.q.f 2
3024.2.q.g 6
3024.2.q.h 6
3024.2.q.i 10
3024.2.q.j 14
3024.2.q.k 22
3024.2.q.l 22
3024.2.r \(\chi_{3024}(1009, \cdot)\) 3024.2.r.a 2 2
3024.2.r.b 2
3024.2.r.c 2
3024.2.r.d 2
3024.2.r.e 4
3024.2.r.f 4
3024.2.r.g 6
3024.2.r.h 6
3024.2.r.i 6
3024.2.r.j 6
3024.2.r.k 6
3024.2.r.l 8
3024.2.r.m 8
3024.2.r.n 10
3024.2.s \(\chi_{3024}(865, \cdot)\) n/a 128 2
3024.2.t \(\chi_{3024}(289, \cdot)\) 3024.2.t.a 2 2
3024.2.t.b 2
3024.2.t.c 2
3024.2.t.d 2
3024.2.t.e 2
3024.2.t.f 2
3024.2.t.g 6
3024.2.t.h 6
3024.2.t.i 10
3024.2.t.j 14
3024.2.t.k 22
3024.2.t.l 22
3024.2.v \(\chi_{3024}(323, \cdot)\) n/a 384 2
3024.2.x \(\chi_{3024}(811, \cdot)\) n/a 512 2
3024.2.z \(\chi_{3024}(757, \cdot)\) n/a 384 2
3024.2.bb \(\chi_{3024}(1133, \cdot)\) n/a 512 2
3024.2.be \(\chi_{3024}(361, \cdot)\) None 0 2
3024.2.bf \(\chi_{3024}(1711, \cdot)\) 3024.2.bf.a 2 2
3024.2.bf.b 2
3024.2.bf.c 2
3024.2.bf.d 2
3024.2.bf.e 4
3024.2.bf.f 4
3024.2.bf.g 24
3024.2.bf.h 24
3024.2.bf.i 32
3024.2.bg \(\chi_{3024}(89, \cdot)\) None 0 2
3024.2.bh \(\chi_{3024}(1871, \cdot)\) 3024.2.bh.a 2 2
3024.2.bh.b 2
3024.2.bh.c 30
3024.2.bh.d 30
3024.2.bh.e 32
3024.2.bm \(\chi_{3024}(1063, \cdot)\) None 0 2
3024.2.bn \(\chi_{3024}(1207, \cdot)\) None 0 2
3024.2.bs \(\chi_{3024}(1783, \cdot)\) None 0 2
3024.2.bt \(\chi_{3024}(593, \cdot)\) n/a 128 2
3024.2.bu \(\chi_{3024}(1943, \cdot)\) None 0 2
3024.2.bz \(\chi_{3024}(71, \cdot)\) None 0 2
3024.2.ca \(\chi_{3024}(2033, \cdot)\) 3024.2.ca.a 2 2
3024.2.ca.b 10
3024.2.ca.c 16
3024.2.ca.d 16
3024.2.ca.e 48
3024.2.cb \(\chi_{3024}(1367, \cdot)\) None 0 2
3024.2.cc \(\chi_{3024}(881, \cdot)\) 3024.2.cc.a 12 2
3024.2.cc.b 16
3024.2.cc.c 16
3024.2.cc.d 48
3024.2.ch \(\chi_{3024}(575, \cdot)\) 3024.2.ch.a 24 2
3024.2.ch.b 24
3024.2.ch.c 24
3024.2.ci \(\chi_{3024}(521, \cdot)\) None 0 2
3024.2.cj \(\chi_{3024}(1439, \cdot)\) 3024.2.cj.a 2 2
3024.2.cj.b 2
3024.2.cj.c 30
3024.2.cj.d 30
3024.2.cj.e 32
3024.2.ck \(\chi_{3024}(1385, \cdot)\) None 0 2
3024.2.cp \(\chi_{3024}(2105, \cdot)\) None 0 2
3024.2.cq \(\chi_{3024}(431, \cdot)\) n/a 128 2
3024.2.cr \(\chi_{3024}(2377, \cdot)\) None 0 2
3024.2.cs \(\chi_{3024}(271, \cdot)\) n/a 128 2
3024.2.cx \(\chi_{3024}(559, \cdot)\) 3024.2.cx.a 2 2
3024.2.cx.b 2
3024.2.cx.c 2
3024.2.cx.d 2
3024.2.cx.e 2
3024.2.cx.f 2
3024.2.cx.g 2
3024.2.cx.h 2
3024.2.cx.i 24
3024.2.cx.j 24
3024.2.cx.k 32
3024.2.cy \(\chi_{3024}(793, \cdot)\) None 0 2
3024.2.cz \(\chi_{3024}(1279, \cdot)\) 3024.2.cz.a 2 2
3024.2.cz.b 2
3024.2.cz.c 2
3024.2.cz.d 2
3024.2.cz.e 4
3024.2.cz.f 4
3024.2.cz.g 24
3024.2.cz.h 24
3024.2.cz.i 32
3024.2.da \(\chi_{3024}(505, \cdot)\) None 0 2
3024.2.df \(\chi_{3024}(17, \cdot)\) 3024.2.df.a 2 2
3024.2.df.b 10
3024.2.df.c 16
3024.2.df.d 16
3024.2.df.e 48
3024.2.dg \(\chi_{3024}(359, \cdot)\) None 0 2
3024.2.dh \(\chi_{3024}(199, \cdot)\) None 0 2
3024.2.dk \(\chi_{3024}(337, \cdot)\) n/a 648 6
3024.2.dl \(\chi_{3024}(193, \cdot)\) n/a 852 6
3024.2.dm \(\chi_{3024}(529, \cdot)\) n/a 852 6
3024.2.dn \(\chi_{3024}(307, \cdot)\) n/a 752 4
3024.2.dp \(\chi_{3024}(827, \cdot)\) n/a 576 4
3024.2.dr \(\chi_{3024}(1045, \cdot)\) n/a 752 4
3024.2.du \(\chi_{3024}(341, \cdot)\) n/a 752 4
3024.2.dv \(\chi_{3024}(269, \cdot)\) n/a 1024 4
3024.2.dx \(\chi_{3024}(109, \cdot)\) n/a 1024 4
3024.2.ea \(\chi_{3024}(37, \cdot)\) n/a 752 4
3024.2.eb \(\chi_{3024}(773, \cdot)\) n/a 752 4
3024.2.ed \(\chi_{3024}(179, \cdot)\) n/a 752 4
3024.2.ef \(\chi_{3024}(1027, \cdot)\) n/a 1024 4
3024.2.ei \(\chi_{3024}(451, \cdot)\) n/a 752 4
3024.2.ek \(\chi_{3024}(611, \cdot)\) n/a 752 4
3024.2.el \(\chi_{3024}(107, \cdot)\) n/a 1024 4
3024.2.en \(\chi_{3024}(19, \cdot)\) n/a 752 4
3024.2.ep \(\chi_{3024}(125, \cdot)\) n/a 752 4
3024.2.er \(\chi_{3024}(253, \cdot)\) n/a 576 4
3024.2.eu \(\chi_{3024}(527, \cdot)\) n/a 864 6
3024.2.ew \(\chi_{3024}(103, \cdot)\) None 0 6
3024.2.ex \(\chi_{3024}(367, \cdot)\) n/a 864 6
3024.2.ez \(\chi_{3024}(23, \cdot)\) None 0 6
3024.2.fb \(\chi_{3024}(185, \cdot)\) None 0 6
3024.2.ff \(\chi_{3024}(41, \cdot)\) None 0 6
3024.2.fi \(\chi_{3024}(457, \cdot)\) None 0 6
3024.2.fj \(\chi_{3024}(209, \cdot)\) n/a 852 6
3024.2.fl \(\chi_{3024}(169, \cdot)\) None 0 6
3024.2.fo \(\chi_{3024}(689, \cdot)\) n/a 852 6
3024.2.fp \(\chi_{3024}(599, \cdot)\) None 0 6
3024.2.fs \(\chi_{3024}(223, \cdot)\) n/a 864 6
3024.2.fu \(\chi_{3024}(407, \cdot)\) None 0 6
3024.2.fv \(\chi_{3024}(31, \cdot)\) n/a 864 6
3024.2.fy \(\chi_{3024}(439, \cdot)\) None 0 6
3024.2.fz \(\chi_{3024}(239, \cdot)\) n/a 648 6
3024.2.gb \(\chi_{3024}(391, \cdot)\) None 0 6
3024.2.ge \(\chi_{3024}(95, \cdot)\) n/a 864 6
3024.2.gg \(\chi_{3024}(257, \cdot)\) n/a 852 6
3024.2.gi \(\chi_{3024}(25, \cdot)\) None 0 6
3024.2.gk \(\chi_{3024}(761, \cdot)\) None 0 6
3024.2.gm \(\chi_{3024}(115, \cdot)\) n/a 6864 12
3024.2.gp \(\chi_{3024}(11, \cdot)\) n/a 6864 12
3024.2.gq \(\chi_{3024}(205, \cdot)\) n/a 6864 12
3024.2.gs \(\chi_{3024}(85, \cdot)\) n/a 5184 12
3024.2.gv \(\chi_{3024}(293, \cdot)\) n/a 6864 12
3024.2.gx \(\chi_{3024}(173, \cdot)\) n/a 6864 12
3024.2.gz \(\chi_{3024}(139, \cdot)\) n/a 6864 12
3024.2.hb \(\chi_{3024}(187, \cdot)\) n/a 6864 12
3024.2.hc \(\chi_{3024}(347, \cdot)\) n/a 6864 12
3024.2.he \(\chi_{3024}(155, \cdot)\) n/a 5184 12
3024.2.hh \(\chi_{3024}(277, \cdot)\) n/a 6864 12
3024.2.hi \(\chi_{3024}(5, \cdot)\) n/a 6864 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1512))\)\(^{\oplus 2}\)