Properties

Label 3150.2
Level 3150
Weight 2
Dimension 60416
Nonzero newspaces 60
Sturm bound 1036800
Trace bound 16

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1036800\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3150))\).

Total New Old
Modular forms 264576 60416 204160
Cusp forms 253825 60416 193409
Eisenstein series 10751 0 10751

Trace form

\(60416q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 26q^{7} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(60416q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 26q^{7} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 22q^{10} \) \(\mathstrut -\mathstrut 74q^{11} \) \(\mathstrut -\mathstrut 32q^{12} \) \(\mathstrut -\mathstrut 66q^{13} \) \(\mathstrut -\mathstrut 64q^{14} \) \(\mathstrut -\mathstrut 48q^{15} \) \(\mathstrut -\mathstrut 196q^{17} \) \(\mathstrut -\mathstrut 76q^{18} \) \(\mathstrut -\mathstrut 158q^{19} \) \(\mathstrut -\mathstrut 32q^{20} \) \(\mathstrut -\mathstrut 90q^{21} \) \(\mathstrut -\mathstrut 138q^{22} \) \(\mathstrut -\mathstrut 236q^{23} \) \(\mathstrut -\mathstrut 6q^{24} \) \(\mathstrut -\mathstrut 158q^{25} \) \(\mathstrut -\mathstrut 70q^{26} \) \(\mathstrut -\mathstrut 132q^{27} \) \(\mathstrut -\mathstrut 56q^{28} \) \(\mathstrut -\mathstrut 260q^{29} \) \(\mathstrut -\mathstrut 188q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut -\mathstrut 38q^{33} \) \(\mathstrut -\mathstrut 100q^{34} \) \(\mathstrut -\mathstrut 76q^{35} \) \(\mathstrut +\mathstrut 58q^{36} \) \(\mathstrut -\mathstrut 314q^{37} \) \(\mathstrut +\mathstrut 96q^{38} \) \(\mathstrut +\mathstrut 220q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 66q^{41} \) \(\mathstrut +\mathstrut 128q^{42} \) \(\mathstrut -\mathstrut 126q^{43} \) \(\mathstrut +\mathstrut 56q^{44} \) \(\mathstrut +\mathstrut 160q^{45} \) \(\mathstrut -\mathstrut 96q^{46} \) \(\mathstrut +\mathstrut 112q^{47} \) \(\mathstrut +\mathstrut 58q^{48} \) \(\mathstrut -\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 114q^{50} \) \(\mathstrut +\mathstrut 210q^{51} \) \(\mathstrut +\mathstrut 18q^{52} \) \(\mathstrut +\mathstrut 246q^{53} \) \(\mathstrut +\mathstrut 246q^{54} \) \(\mathstrut -\mathstrut 144q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 218q^{57} \) \(\mathstrut +\mathstrut 76q^{58} \) \(\mathstrut +\mathstrut 80q^{59} \) \(\mathstrut +\mathstrut 64q^{60} \) \(\mathstrut +\mathstrut 42q^{61} \) \(\mathstrut +\mathstrut 396q^{62} \) \(\mathstrut +\mathstrut 252q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 434q^{65} \) \(\mathstrut +\mathstrut 144q^{66} \) \(\mathstrut +\mathstrut 150q^{67} \) \(\mathstrut +\mathstrut 294q^{68} \) \(\mathstrut +\mathstrut 412q^{69} \) \(\mathstrut +\mathstrut 216q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 6q^{72} \) \(\mathstrut +\mathstrut 208q^{73} \) \(\mathstrut +\mathstrut 496q^{74} \) \(\mathstrut +\mathstrut 592q^{75} \) \(\mathstrut +\mathstrut 64q^{76} \) \(\mathstrut +\mathstrut 402q^{77} \) \(\mathstrut +\mathstrut 300q^{78} \) \(\mathstrut +\mathstrut 196q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 262q^{81} \) \(\mathstrut +\mathstrut 392q^{82} \) \(\mathstrut +\mathstrut 782q^{83} \) \(\mathstrut +\mathstrut 78q^{84} \) \(\mathstrut +\mathstrut 322q^{85} \) \(\mathstrut +\mathstrut 242q^{86} \) \(\mathstrut +\mathstrut 644q^{87} \) \(\mathstrut +\mathstrut 110q^{88} \) \(\mathstrut +\mathstrut 1138q^{89} \) \(\mathstrut +\mathstrut 320q^{90} \) \(\mathstrut +\mathstrut 494q^{91} \) \(\mathstrut +\mathstrut 276q^{92} \) \(\mathstrut +\mathstrut 772q^{93} \) \(\mathstrut +\mathstrut 464q^{94} \) \(\mathstrut +\mathstrut 520q^{95} \) \(\mathstrut +\mathstrut 52q^{96} \) \(\mathstrut +\mathstrut 554q^{97} \) \(\mathstrut +\mathstrut 696q^{98} \) \(\mathstrut +\mathstrut 676q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3150))\)

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
3150.2.a \(\chi_{3150}(1, \cdot)\) 3150.2.a.a 1 1
3150.2.a.b 1
3150.2.a.c 1
3150.2.a.d 1
3150.2.a.e 1
3150.2.a.f 1
3150.2.a.g 1
3150.2.a.h 1
3150.2.a.i 1
3150.2.a.j 1
3150.2.a.k 1
3150.2.a.l 1
3150.2.a.m 1
3150.2.a.n 1
3150.2.a.o 1
3150.2.a.p 1
3150.2.a.q 1
3150.2.a.r 1
3150.2.a.s 1
3150.2.a.t 1
3150.2.a.u 1
3150.2.a.v 1
3150.2.a.w 1
3150.2.a.x 1
3150.2.a.y 1
3150.2.a.z 1
3150.2.a.ba 1
3150.2.a.bb 1
3150.2.a.bc 1
3150.2.a.bd 1
3150.2.a.be 1
3150.2.a.bf 1
3150.2.a.bg 1
3150.2.a.bh 1
3150.2.a.bi 1
3150.2.a.bj 1
3150.2.a.bk 1
3150.2.a.bl 1
3150.2.a.bm 1
3150.2.a.bn 1
3150.2.a.bo 1
3150.2.a.bp 1
3150.2.a.bq 1
3150.2.a.br 1
3150.2.a.bs 2
3150.2.a.bt 2
3150.2.b \(\chi_{3150}(251, \cdot)\) 3150.2.b.a 8 1
3150.2.b.b 8
3150.2.b.c 8
3150.2.b.d 8
3150.2.b.e 8
3150.2.b.f 8
3150.2.d \(\chi_{3150}(3149, \cdot)\) 3150.2.d.a 8 1
3150.2.d.b 8
3150.2.d.c 8
3150.2.d.d 8
3150.2.d.e 8
3150.2.d.f 8
3150.2.g \(\chi_{3150}(2899, \cdot)\) 3150.2.g.a 2 1
3150.2.g.b 2
3150.2.g.c 2
3150.2.g.d 2
3150.2.g.e 2
3150.2.g.f 2
3150.2.g.g 2
3150.2.g.h 2
3150.2.g.i 2
3150.2.g.j 2
3150.2.g.k 2
3150.2.g.l 2
3150.2.g.m 2
3150.2.g.n 2
3150.2.g.o 2
3150.2.g.p 2
3150.2.g.q 2
3150.2.g.r 2
3150.2.g.s 2
3150.2.g.t 2
3150.2.g.u 2
3150.2.g.v 2
3150.2.i \(\chi_{3150}(151, \cdot)\) n/a 304 2
3150.2.j \(\chi_{3150}(1051, \cdot)\) n/a 228 2
3150.2.k \(\chi_{3150}(1801, \cdot)\) n/a 128 2
3150.2.l \(\chi_{3150}(1201, \cdot)\) n/a 304 2
3150.2.m \(\chi_{3150}(1457, \cdot)\) 3150.2.m.a 4 2
3150.2.m.b 4
3150.2.m.c 4
3150.2.m.d 4
3150.2.m.e 4
3150.2.m.f 4
3150.2.m.g 8
3150.2.m.h 8
3150.2.m.i 8
3150.2.m.j 8
3150.2.m.k 8
3150.2.m.l 8
3150.2.p \(\chi_{3150}(307, \cdot)\) n/a 120 2
3150.2.q \(\chi_{3150}(631, \cdot)\) n/a 296 4
3150.2.s \(\chi_{3150}(299, \cdot)\) n/a 288 2
3150.2.u \(\chi_{3150}(551, \cdot)\) n/a 304 2
3150.2.v \(\chi_{3150}(1549, \cdot)\) n/a 120 2
3150.2.ba \(\chi_{3150}(799, \cdot)\) n/a 216 2
3150.2.bb \(\chi_{3150}(499, \cdot)\) n/a 288 2
3150.2.bf \(\chi_{3150}(1151, \cdot)\) n/a 104 2
3150.2.bg \(\chi_{3150}(1049, \cdot)\) n/a 288 2
3150.2.bj \(\chi_{3150}(2399, \cdot)\) n/a 288 2
3150.2.bl \(\chi_{3150}(101, \cdot)\) n/a 304 2
3150.2.bm \(\chi_{3150}(1301, \cdot)\) n/a 304 2
3150.2.bp \(\chi_{3150}(899, \cdot)\) 3150.2.bp.a 8 2
3150.2.bp.b 8
3150.2.bp.c 8
3150.2.bp.d 8
3150.2.bp.e 8
3150.2.bp.f 8
3150.2.bp.g 24
3150.2.bp.h 24
3150.2.br \(\chi_{3150}(949, \cdot)\) n/a 288 2
3150.2.bu \(\chi_{3150}(379, \cdot)\) n/a 304 4
3150.2.bx \(\chi_{3150}(629, \cdot)\) n/a 320 4
3150.2.bz \(\chi_{3150}(881, \cdot)\) n/a 320 4
3150.2.cb \(\chi_{3150}(443, \cdot)\) n/a 576 4
3150.2.cd \(\chi_{3150}(1207, \cdot)\) n/a 240 4
3150.2.ce \(\chi_{3150}(493, \cdot)\) n/a 576 4
3150.2.ch \(\chi_{3150}(643, \cdot)\) n/a 576 4
3150.2.ci \(\chi_{3150}(407, \cdot)\) n/a 432 4
3150.2.cl \(\chi_{3150}(893, \cdot)\) n/a 576 4
3150.2.cm \(\chi_{3150}(107, \cdot)\) n/a 192 4
3150.2.co \(\chi_{3150}(157, \cdot)\) n/a 576 4
3150.2.cq \(\chi_{3150}(331, \cdot)\) n/a 1920 8
3150.2.cr \(\chi_{3150}(361, \cdot)\) n/a 800 8
3150.2.cs \(\chi_{3150}(211, \cdot)\) n/a 1440 8
3150.2.ct \(\chi_{3150}(121, \cdot)\) n/a 1920 8
3150.2.cu \(\chi_{3150}(433, \cdot)\) n/a 800 8
3150.2.cx \(\chi_{3150}(197, \cdot)\) n/a 480 8
3150.2.cz \(\chi_{3150}(79, \cdot)\) n/a 1920 8
3150.2.db \(\chi_{3150}(89, \cdot)\) n/a 640 8
3150.2.de \(\chi_{3150}(41, \cdot)\) n/a 1920 8
3150.2.df \(\chi_{3150}(131, \cdot)\) n/a 1920 8
3150.2.dh \(\chi_{3150}(479, \cdot)\) n/a 1920 8
3150.2.dk \(\chi_{3150}(209, \cdot)\) n/a 1920 8
3150.2.dl \(\chi_{3150}(341, \cdot)\) n/a 640 8
3150.2.dp \(\chi_{3150}(529, \cdot)\) n/a 1920 8
3150.2.dq \(\chi_{3150}(169, \cdot)\) n/a 1440 8
3150.2.dv \(\chi_{3150}(109, \cdot)\) n/a 800 8
3150.2.dw \(\chi_{3150}(311, \cdot)\) n/a 1920 8
3150.2.dy \(\chi_{3150}(59, \cdot)\) n/a 1920 8
3150.2.eb \(\chi_{3150}(187, \cdot)\) n/a 3840 16
3150.2.ed \(\chi_{3150}(53, \cdot)\) n/a 1280 16
3150.2.ee \(\chi_{3150}(23, \cdot)\) n/a 3840 16
3150.2.eh \(\chi_{3150}(113, \cdot)\) n/a 2880 16
3150.2.ei \(\chi_{3150}(13, \cdot)\) n/a 3840 16
3150.2.el \(\chi_{3150}(103, \cdot)\) n/a 3840 16
3150.2.em \(\chi_{3150}(73, \cdot)\) n/a 1600 16
3150.2.eo \(\chi_{3150}(317, \cdot)\) n/a 3840 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1575))\)\(^{\oplus 2}\)