# Properties

 Label 3150.3 Level 3150 Weight 3 Dimension 120828 Nonzero newspaces 60 Sturm bound 1555200 Trace bound 16

## Defining parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$60$$ Sturm bound: $$1555200$$ Trace bound: $$16$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(3150))$$.

Total New Old
Modular forms 523776 120828 402948
Cusp forms 513024 120828 392196
Eisenstein series 10752 0 10752

## Trace form

 $$120828 q - 8 q^{2} - 4 q^{4} + 24 q^{6} + 22 q^{7} + 16 q^{8} + 136 q^{9} + O(q^{10})$$ $$120828 q - 8 q^{2} - 4 q^{4} + 24 q^{6} + 22 q^{7} + 16 q^{8} + 136 q^{9} + 108 q^{10} + 302 q^{11} + 40 q^{12} + 196 q^{13} + 72 q^{14} - 48 q^{15} - 8 q^{16} - 54 q^{17} - 160 q^{18} - 34 q^{19} - 112 q^{20} - 90 q^{21} - 240 q^{22} + 34 q^{23} - 48 q^{24} + 252 q^{25} - 8 q^{26} - 60 q^{27} + 84 q^{28} - 340 q^{29} - 254 q^{31} - 48 q^{32} - 1004 q^{33} - 300 q^{34} - 776 q^{35} - 536 q^{36} - 6 q^{37} - 988 q^{38} - 1964 q^{39} + 24 q^{40} - 1316 q^{41} - 208 q^{42} - 444 q^{43} - 444 q^{44} + 160 q^{45} - 940 q^{46} + 274 q^{47} + 208 q^{48} - 66 q^{49} + 484 q^{50} + 1296 q^{51} - 56 q^{52} + 694 q^{53} + 1272 q^{54} - 944 q^{55} + 200 q^{56} + 1856 q^{57} + 112 q^{58} - 710 q^{59} - 896 q^{60} + 222 q^{61} - 2432 q^{62} - 1566 q^{63} + 128 q^{64} - 4276 q^{65} + 144 q^{66} - 1922 q^{67} - 988 q^{68} - 1028 q^{69} - 744 q^{70} - 488 q^{71} + 192 q^{72} - 1402 q^{73} + 384 q^{74} - 1088 q^{75} - 40 q^{76} - 268 q^{77} + 1440 q^{78} + 1070 q^{79} - 1520 q^{81} + 1712 q^{82} + 2764 q^{83} + 864 q^{84} + 4392 q^{85} - 384 q^{86} - 208 q^{87} - 1288 q^{88} - 422 q^{89} + 1280 q^{90} - 5244 q^{91} - 560 q^{92} - 2240 q^{93} - 2900 q^{94} - 2480 q^{95} - 512 q^{96} - 5412 q^{97} - 3648 q^{98} + 484 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(3150))$$

We only show spaces with odd 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
3150.3.c $$\chi_{3150}(449, \cdot)$$ 3150.3.c.a 8 1
3150.3.c.b 8
3150.3.c.c 8
3150.3.c.d 16
3150.3.c.e 16
3150.3.c.f 16
3150.3.e $$\chi_{3150}(701, \cdot)$$ 3150.3.e.a 4 1
3150.3.e.b 4
3150.3.e.c 4
3150.3.e.d 4
3150.3.e.e 4
3150.3.e.f 8
3150.3.e.g 8
3150.3.e.h 8
3150.3.e.i 8
3150.3.e.j 12
3150.3.e.k 12
3150.3.f $$\chi_{3150}(2701, \cdot)$$ n/a 128 1
3150.3.h $$\chi_{3150}(2449, \cdot)$$ n/a 120 1
3150.3.n $$\chi_{3150}(1007, \cdot)$$ n/a 192 2
3150.3.o $$\chi_{3150}(757, \cdot)$$ n/a 180 2
3150.3.r $$\chi_{3150}(851, \cdot)$$ n/a 608 2
3150.3.t $$\chi_{3150}(599, \cdot)$$ n/a 576 2
3150.3.w $$\chi_{3150}(451, \cdot)$$ n/a 252 2
3150.3.x $$\chi_{3150}(1249, \cdot)$$ n/a 576 2
3150.3.y $$\chi_{3150}(349, \cdot)$$ n/a 576 2
3150.3.z $$\chi_{3150}(601, \cdot)$$ n/a 608 2
3150.3.bc $$\chi_{3150}(1501, \cdot)$$ n/a 608 2
3150.3.bd $$\chi_{3150}(199, \cdot)$$ n/a 240 2
3150.3.be $$\chi_{3150}(2249, \cdot)$$ n/a 192 2
3150.3.bh $$\chi_{3150}(1751, \cdot)$$ n/a 456 2
3150.3.bi $$\chi_{3150}(401, \cdot)$$ n/a 608 2
3150.3.bk $$\chi_{3150}(149, \cdot)$$ n/a 576 2
3150.3.bn $$\chi_{3150}(1499, \cdot)$$ n/a 432 2
3150.3.bo $$\chi_{3150}(2501, \cdot)$$ n/a 200 2
3150.3.bq $$\chi_{3150}(1699, \cdot)$$ n/a 576 2
3150.3.bs $$\chi_{3150}(1951, \cdot)$$ n/a 608 2
3150.3.bt $$\chi_{3150}(559, \cdot)$$ n/a 800 4
3150.3.bv $$\chi_{3150}(181, \cdot)$$ n/a 800 4
3150.3.bw $$\chi_{3150}(71, \cdot)$$ n/a 480 4
3150.3.by $$\chi_{3150}(1079, \cdot)$$ n/a 480 4
3150.3.ca $$\chi_{3150}(1193, \cdot)$$ n/a 1152 4
3150.3.cc $$\chi_{3150}(43, \cdot)$$ n/a 864 4
3150.3.cf $$\chi_{3150}(793, \cdot)$$ n/a 480 4
3150.3.cg $$\chi_{3150}(907, \cdot)$$ n/a 1152 4
3150.3.cj $$\chi_{3150}(257, \cdot)$$ n/a 1152 4
3150.3.ck $$\chi_{3150}(143, \cdot)$$ n/a 384 4
3150.3.cn $$\chi_{3150}(293, \cdot)$$ n/a 1152 4
3150.3.cp $$\chi_{3150}(193, \cdot)$$ n/a 1152 4
3150.3.cv $$\chi_{3150}(127, \cdot)$$ n/a 1200 8
3150.3.cw $$\chi_{3150}(377, \cdot)$$ n/a 1280 8
3150.3.cy $$\chi_{3150}(31, \cdot)$$ n/a 3840 8
3150.3.da $$\chi_{3150}(409, \cdot)$$ n/a 3840 8
3150.3.dc $$\chi_{3150}(431, \cdot)$$ n/a 1280 8
3150.3.dd $$\chi_{3150}(29, \cdot)$$ n/a 2880 8
3150.3.dg $$\chi_{3150}(389, \cdot)$$ n/a 3840 8
3150.3.di $$\chi_{3150}(11, \cdot)$$ n/a 3840 8
3150.3.dj $$\chi_{3150}(281, \cdot)$$ n/a 2880 8
3150.3.dm $$\chi_{3150}(179, \cdot)$$ n/a 1280 8
3150.3.dn $$\chi_{3150}(19, \cdot)$$ n/a 1600 8
3150.3.do $$\chi_{3150}(241, \cdot)$$ n/a 3840 8
3150.3.dr $$\chi_{3150}(391, \cdot)$$ n/a 3840 8
3150.3.ds $$\chi_{3150}(139, \cdot)$$ n/a 3840 8
3150.3.dt $$\chi_{3150}(229, \cdot)$$ n/a 3840 8
3150.3.du $$\chi_{3150}(271, \cdot)$$ n/a 1600 8
3150.3.dx $$\chi_{3150}(569, \cdot)$$ n/a 3840 8
3150.3.dz $$\chi_{3150}(191, \cdot)$$ n/a 3840 8
3150.3.ea $$\chi_{3150}(67, \cdot)$$ n/a 7680 16
3150.3.ec $$\chi_{3150}(83, \cdot)$$ n/a 7680 16
3150.3.ef $$\chi_{3150}(17, \cdot)$$ n/a 2560 16
3150.3.eg $$\chi_{3150}(227, \cdot)$$ n/a 7680 16
3150.3.ej $$\chi_{3150}(247, \cdot)$$ n/a 7680 16
3150.3.ek $$\chi_{3150}(37, \cdot)$$ n/a 3200 16
3150.3.en $$\chi_{3150}(337, \cdot)$$ n/a 5760 16
3150.3.ep $$\chi_{3150}(47, \cdot)$$ n/a 7680 16

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(3150))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(3150)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 18}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(630))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(1050))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(1575))$$$$^{\oplus 2}$$