Properties

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

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

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