# Properties

 Label 2850.2 Level 2850 Weight 2 Dimension 49496 Nonzero newspaces 36 Sturm bound 864000 Trace bound 15

## Defining parameters

 Level: $$N$$ = $$2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$864000$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2850))$$.

Total New Old
Modular forms 220032 49496 170536
Cusp forms 211969 49496 162473
Eisenstein series 8063 0 8063

## Trace form

 $$49496 q - 6 q^{2} - 14 q^{3} - 6 q^{4} - 20 q^{5} - 14 q^{6} - 48 q^{7} - 6 q^{8} - 6 q^{9} + O(q^{10})$$ $$49496 q - 6 q^{2} - 14 q^{3} - 6 q^{4} - 20 q^{5} - 14 q^{6} - 48 q^{7} - 6 q^{8} - 6 q^{9} - 4 q^{10} - 8 q^{11} + 12 q^{12} - 68 q^{13} - 20 q^{14} + 8 q^{15} - 6 q^{16} + 32 q^{17} + 46 q^{18} - 32 q^{19} + 16 q^{20} + 22 q^{21} + 66 q^{22} + 76 q^{23} + 26 q^{24} + 172 q^{25} - 40 q^{26} - 29 q^{27} + 20 q^{28} + 40 q^{29} + 40 q^{30} - 4 q^{31} + 14 q^{32} - 14 q^{33} + 56 q^{34} + 16 q^{35} - 6 q^{36} + 12 q^{37} - 12 q^{38} + 54 q^{39} + 12 q^{40} - 48 q^{41} + 16 q^{42} + 80 q^{43} - 40 q^{44} + 140 q^{45} + 48 q^{46} + 28 q^{47} + 27 q^{48} + 90 q^{49} - 36 q^{50} + 141 q^{51} - 20 q^{52} + 48 q^{53} + 40 q^{54} + 48 q^{55} - 16 q^{56} + 110 q^{57} - 116 q^{58} - 40 q^{59} - 64 q^{60} - 176 q^{61} - 96 q^{62} - 102 q^{63} - 6 q^{64} - 148 q^{65} - 24 q^{66} - 288 q^{67} - 12 q^{68} - 306 q^{69} - 96 q^{70} - 84 q^{71} - 29 q^{72} - 274 q^{73} - 68 q^{74} - 328 q^{75} + 4 q^{76} + 24 q^{77} + 16 q^{78} + 292 q^{79} - 20 q^{80} + 466 q^{81} + 380 q^{82} + 680 q^{83} + 242 q^{84} + 508 q^{85} + 464 q^{86} + 848 q^{87} - 40 q^{88} + 712 q^{89} + 252 q^{90} + 960 q^{91} + 456 q^{92} + 1042 q^{93} + 848 q^{94} + 416 q^{95} + 18 q^{96} + 696 q^{97} + 858 q^{98} + 1031 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2850))$$

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
2850.2.a $$\chi_{2850}(1, \cdot)$$ 2850.2.a.a 1 1
2850.2.a.b 1
2850.2.a.c 1
2850.2.a.d 1
2850.2.a.e 1
2850.2.a.f 1
2850.2.a.g 1
2850.2.a.h 1
2850.2.a.i 1
2850.2.a.j 1
2850.2.a.k 1
2850.2.a.l 1
2850.2.a.m 1
2850.2.a.n 1
2850.2.a.o 1
2850.2.a.p 1
2850.2.a.q 1
2850.2.a.r 1
2850.2.a.s 1
2850.2.a.t 1
2850.2.a.u 1
2850.2.a.v 1
2850.2.a.w 1
2850.2.a.x 1
2850.2.a.y 1
2850.2.a.z 1
2850.2.a.ba 1
2850.2.a.bb 1
2850.2.a.bc 2
2850.2.a.bd 2
2850.2.a.be 2
2850.2.a.bf 2
2850.2.a.bg 2
2850.2.a.bh 2
2850.2.a.bi 2
2850.2.a.bj 2
2850.2.a.bk 3
2850.2.a.bl 3
2850.2.a.bm 3
2850.2.a.bn 3
2850.2.c $$\chi_{2850}(2849, \cdot)$$ n/a 120 1
2850.2.d $$\chi_{2850}(799, \cdot)$$ 2850.2.d.a 2 1
2850.2.d.b 2
2850.2.d.c 2
2850.2.d.d 2
2850.2.d.e 2
2850.2.d.f 2
2850.2.d.g 2
2850.2.d.h 2
2850.2.d.i 2
2850.2.d.j 2
2850.2.d.k 2
2850.2.d.l 2
2850.2.d.m 2
2850.2.d.n 2
2850.2.d.o 2
2850.2.d.p 2
2850.2.d.q 2
2850.2.d.r 2
2850.2.d.s 2
2850.2.d.t 2
2850.2.d.u 4
2850.2.d.v 4
2850.2.d.w 4
2850.2.d.x 4
2850.2.f $$\chi_{2850}(2051, \cdot)$$ n/a 128 1
2850.2.i $$\chi_{2850}(2101, \cdot)$$ n/a 124 2
2850.2.k $$\chi_{2850}(2243, \cdot)$$ n/a 216 2
2850.2.m $$\chi_{2850}(493, \cdot)$$ n/a 120 2
2850.2.n $$\chi_{2850}(571, \cdot)$$ n/a 368 4
2850.2.o $$\chi_{2850}(449, \cdot)$$ n/a 240 2
2850.2.r $$\chi_{2850}(49, \cdot)$$ n/a 120 2
2850.2.t $$\chi_{2850}(2501, \cdot)$$ n/a 256 2
2850.2.v $$\chi_{2850}(301, \cdot)$$ n/a 384 6
2850.2.x $$\chi_{2850}(229, \cdot)$$ n/a 352 4
2850.2.y $$\chi_{2850}(569, \cdot)$$ n/a 800 4
2850.2.bc $$\chi_{2850}(341, \cdot)$$ n/a 800 4
2850.2.bd $$\chi_{2850}(1493, \cdot)$$ n/a 480 4
2850.2.bf $$\chi_{2850}(943, \cdot)$$ n/a 240 4
2850.2.bh $$\chi_{2850}(121, \cdot)$$ n/a 800 8
2850.2.bk $$\chi_{2850}(401, \cdot)$$ n/a 756 6
2850.2.bl $$\chi_{2850}(199, \cdot)$$ n/a 360 6
2850.2.bo $$\chi_{2850}(299, \cdot)$$ n/a 720 6
2850.2.bp $$\chi_{2850}(37, \cdot)$$ n/a 800 8
2850.2.br $$\chi_{2850}(77, \cdot)$$ n/a 1440 8
2850.2.bt $$\chi_{2850}(619, \cdot)$$ n/a 800 8
2850.2.bw $$\chi_{2850}(179, \cdot)$$ n/a 1600 8
2850.2.by $$\chi_{2850}(221, \cdot)$$ n/a 1600 8
2850.2.cb $$\chi_{2850}(193, \cdot)$$ n/a 720 12
2850.2.cc $$\chi_{2850}(443, \cdot)$$ n/a 1440 12
2850.2.ce $$\chi_{2850}(61, \cdot)$$ n/a 2400 24
2850.2.cg $$\chi_{2850}(103, \cdot)$$ n/a 1600 16
2850.2.ci $$\chi_{2850}(83, \cdot)$$ n/a 3200 16
2850.2.cj $$\chi_{2850}(41, \cdot)$$ n/a 4800 24
2850.2.cm $$\chi_{2850}(29, \cdot)$$ n/a 4800 24
2850.2.cp $$\chi_{2850}(139, \cdot)$$ n/a 2400 24
2850.2.cr $$\chi_{2850}(17, \cdot)$$ n/a 9600 48
2850.2.cs $$\chi_{2850}(13, \cdot)$$ n/a 4800 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2850))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2850)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(950))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1425))$$$$^{\oplus 2}$$