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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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 \(\chi_{3150}(1151, \cdot)\) 3150.2.bf.a 8 2
3150.2.bf.b 8
3150.2.bf.c 8
3150.2.bf.d 24
3150.2.bf.e 24
3150.2.bf.f 32
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

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