# Properties

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

## 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

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

## 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 $$\chi_{3150}(1151, \cdot)$$ 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

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