# Properties

 Label 200.6 Level 200 Weight 6 Dimension 3070 Nonzero newspaces 10 Sturm bound 14400 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$200 = 2^{3} \cdot 5^{2}$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$10$$ Sturm bound: $$14400$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(200))$$.

Total New Old
Modular forms 6168 3152 3016
Cusp forms 5832 3070 2762
Eisenstein series 336 82 254

## Trace form

 $$3070 q - 14 q^{2} + 8 q^{3} + 8 q^{4} + 41 q^{5} - 136 q^{6} - 92 q^{7} - 260 q^{8} + 779 q^{9} + O(q^{10})$$ $$3070 q - 14 q^{2} + 8 q^{3} + 8 q^{4} + 41 q^{5} - 136 q^{6} - 92 q^{7} - 260 q^{8} + 779 q^{9} - 16 q^{10} + 144 q^{11} - 380 q^{12} - 1878 q^{13} + 3100 q^{14} + 2456 q^{15} - 292 q^{16} + 614 q^{17} - 10434 q^{18} - 5640 q^{19} - 6836 q^{20} - 1360 q^{21} - 4488 q^{22} - 380 q^{23} + 25740 q^{24} - 247 q^{25} + 29408 q^{26} + 15044 q^{27} + 348 q^{28} - 8790 q^{29} - 9780 q^{30} + 19644 q^{31} - 45764 q^{32} + 22664 q^{33} - 54000 q^{34} - 10348 q^{35} + 15736 q^{36} - 62491 q^{37} + 90248 q^{38} - 51252 q^{39} + 59224 q^{40} - 4774 q^{41} + 28524 q^{42} + 24152 q^{43} - 78700 q^{44} + 15341 q^{45} - 232180 q^{46} - 3804 q^{47} - 116708 q^{48} + 39098 q^{49} + 103364 q^{50} + 58740 q^{51} + 323380 q^{52} - 23891 q^{53} + 138420 q^{54} + 60312 q^{55} - 150212 q^{56} + 93576 q^{57} - 302564 q^{58} - 200024 q^{59} - 201180 q^{60} - 111962 q^{61} - 235636 q^{62} - 288612 q^{63} + 242156 q^{64} - 75719 q^{65} + 338164 q^{66} + 129768 q^{67} + 262124 q^{68} + 441104 q^{69} + 34980 q^{70} + 189268 q^{71} - 219528 q^{72} + 338238 q^{73} - 278516 q^{74} - 54584 q^{75} - 31056 q^{76} - 448864 q^{77} + 653324 q^{78} - 181412 q^{79} + 233924 q^{80} - 1074297 q^{81} + 1447904 q^{82} + 545604 q^{83} + 492556 q^{84} - 134767 q^{85} - 384080 q^{86} - 506692 q^{87} - 2166676 q^{88} + 1043529 q^{89} - 2325916 q^{90} - 306012 q^{91} - 1052524 q^{92} + 340600 q^{93} + 140732 q^{94} + 412992 q^{95} + 653572 q^{96} - 651822 q^{97} + 2392634 q^{98} + 286056 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(200))$$

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
200.6.a $$\chi_{200}(1, \cdot)$$ 200.6.a.a 1 1
200.6.a.b 1
200.6.a.c 1
200.6.a.d 1
200.6.a.e 2
200.6.a.f 2
200.6.a.g 2
200.6.a.h 3
200.6.a.i 3
200.6.a.j 4
200.6.a.k 4
200.6.c $$\chi_{200}(49, \cdot)$$ 200.6.c.a 2 1
200.6.c.b 2
200.6.c.c 2
200.6.c.d 2
200.6.c.e 4
200.6.c.f 4
200.6.c.g 6
200.6.d $$\chi_{200}(101, \cdot)$$ 200.6.d.a 4 1
200.6.d.b 20
200.6.d.c 20
200.6.d.d 20
200.6.d.e 28
200.6.f $$\chi_{200}(149, \cdot)$$ 200.6.f.a 8 1
200.6.f.b 20
200.6.f.c 20
200.6.f.d 40
200.6.j $$\chi_{200}(7, \cdot)$$ None 0 2
200.6.k $$\chi_{200}(43, \cdot)$$ n/a 176 2
200.6.m $$\chi_{200}(41, \cdot)$$ n/a 148 4
200.6.o $$\chi_{200}(29, \cdot)$$ n/a 592 4
200.6.q $$\chi_{200}(9, \cdot)$$ n/a 152 4
200.6.t $$\chi_{200}(21, \cdot)$$ n/a 592 4
200.6.v $$\chi_{200}(3, \cdot)$$ n/a 1184 8
200.6.w $$\chi_{200}(23, \cdot)$$ None 0 8

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(200))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(200)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 2}$$