# Properties

 Label 3200.2 Level 3200 Weight 2 Dimension 158280 Nonzero newspaces 36 Sturm bound 1228800 Trace bound 33

## Defining parameters

 Level: $$N$$ = $$3200 = 2^{7} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$1228800$$ Trace bound: $$33$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3200))$$.

Total New Old
Modular forms 311680 160248 151432
Cusp forms 302721 158280 144441
Eisenstein series 8959 1968 6991

## Trace form

 $$158280 q - 208 q^{2} - 156 q^{3} - 208 q^{4} - 256 q^{5} - 336 q^{6} - 156 q^{7} - 208 q^{8} - 260 q^{9} + O(q^{10})$$ $$158280 q - 208 q^{2} - 156 q^{3} - 208 q^{4} - 256 q^{5} - 336 q^{6} - 156 q^{7} - 208 q^{8} - 260 q^{9} - 256 q^{10} - 252 q^{11} - 208 q^{12} - 208 q^{13} - 208 q^{14} - 192 q^{15} - 336 q^{16} - 312 q^{17} - 208 q^{18} - 156 q^{19} - 256 q^{20} - 348 q^{21} - 208 q^{22} - 164 q^{23} - 208 q^{24} - 320 q^{25} - 656 q^{26} - 180 q^{27} - 208 q^{28} - 224 q^{29} - 256 q^{30} - 272 q^{31} - 208 q^{32} - 448 q^{33} - 208 q^{34} - 192 q^{35} - 336 q^{36} - 224 q^{37} - 208 q^{38} - 180 q^{39} - 256 q^{40} - 436 q^{41} - 208 q^{42} - 164 q^{43} - 208 q^{44} - 256 q^{45} - 336 q^{46} - 160 q^{47} - 208 q^{48} - 284 q^{49} - 256 q^{50} - 488 q^{51} - 112 q^{52} - 176 q^{53} - 80 q^{54} - 192 q^{55} - 224 q^{56} - 196 q^{57} - 64 q^{58} - 124 q^{59} - 256 q^{60} - 272 q^{61} - 112 q^{62} - 96 q^{63} - 16 q^{64} - 256 q^{65} - 144 q^{66} - 116 q^{67} - 112 q^{68} - 156 q^{69} - 256 q^{70} - 220 q^{71} - 64 q^{72} - 196 q^{73} - 96 q^{74} - 192 q^{75} - 528 q^{76} - 204 q^{77} - 112 q^{78} - 128 q^{79} - 256 q^{80} - 500 q^{81} - 208 q^{82} - 196 q^{83} - 208 q^{84} - 256 q^{85} - 336 q^{86} - 212 q^{87} - 208 q^{88} - 324 q^{89} - 256 q^{90} - 300 q^{91} - 208 q^{92} - 256 q^{93} - 208 q^{94} - 192 q^{95} - 336 q^{96} - 480 q^{97} - 208 q^{98} - 208 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3200))$$

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
3200.2.a $$\chi_{3200}(1, \cdot)$$ 3200.2.a.a 1 1
3200.2.a.b 1
3200.2.a.c 1
3200.2.a.d 1
3200.2.a.e 1
3200.2.a.f 1
3200.2.a.g 1
3200.2.a.h 1
3200.2.a.i 1
3200.2.a.j 1
3200.2.a.k 1
3200.2.a.l 1
3200.2.a.m 1
3200.2.a.n 1
3200.2.a.o 1
3200.2.a.p 1
3200.2.a.q 1
3200.2.a.r 1
3200.2.a.s 1
3200.2.a.t 1
3200.2.a.u 1
3200.2.a.v 1
3200.2.a.w 1
3200.2.a.x 1
3200.2.a.y 1
3200.2.a.z 1
3200.2.a.ba 1
3200.2.a.bb 1
3200.2.a.bc 2
3200.2.a.bd 2
3200.2.a.be 2
3200.2.a.bf 2
3200.2.a.bg 2
3200.2.a.bh 2
3200.2.a.bi 2
3200.2.a.bj 2
3200.2.a.bk 2
3200.2.a.bl 2
3200.2.a.bm 2
3200.2.a.bn 2
3200.2.a.bo 3
3200.2.a.bp 3
3200.2.a.bq 3
3200.2.a.br 3
3200.2.a.bs 3
3200.2.a.bt 3
3200.2.a.bu 3
3200.2.a.bv 3
3200.2.c $$\chi_{3200}(2049, \cdot)$$ 3200.2.c.a 2 1
3200.2.c.b 2
3200.2.c.c 2
3200.2.c.d 2
3200.2.c.e 2
3200.2.c.f 2
3200.2.c.g 2
3200.2.c.h 2
3200.2.c.i 2
3200.2.c.j 2
3200.2.c.k 2
3200.2.c.l 2
3200.2.c.m 2
3200.2.c.n 2
3200.2.c.o 2
3200.2.c.p 2
3200.2.c.q 2
3200.2.c.r 2
3200.2.c.s 2
3200.2.c.t 2
3200.2.c.u 4
3200.2.c.v 4
3200.2.c.w 4
3200.2.c.x 4
3200.2.c.y 4
3200.2.c.z 4
3200.2.c.ba 4
3200.2.c.bb 4
3200.2.d $$\chi_{3200}(1601, \cdot)$$ 3200.2.d.a 2 1
3200.2.d.b 2
3200.2.d.c 2
3200.2.d.d 2
3200.2.d.e 2
3200.2.d.f 2
3200.2.d.g 2
3200.2.d.h 2
3200.2.d.i 4
3200.2.d.j 4
3200.2.d.k 4
3200.2.d.l 4
3200.2.d.m 4
3200.2.d.n 4
3200.2.d.o 4
3200.2.d.p 4
3200.2.d.q 4
3200.2.d.r 4
3200.2.d.s 4
3200.2.d.t 4
3200.2.d.u 4
3200.2.d.v 4
3200.2.d.w 4
3200.2.f $$\chi_{3200}(449, \cdot)$$ 3200.2.f.a 2 1
3200.2.f.b 2
3200.2.f.c 2
3200.2.f.d 2
3200.2.f.e 2
3200.2.f.f 2
3200.2.f.g 4
3200.2.f.h 4
3200.2.f.i 4
3200.2.f.j 4
3200.2.f.k 4
3200.2.f.l 4
3200.2.f.m 4
3200.2.f.n 4
3200.2.f.o 4
3200.2.f.p 4
3200.2.f.q 4
3200.2.f.r 8
3200.2.f.s 8
3200.2.j $$\chi_{3200}(543, \cdot)$$ n/a 136 2
3200.2.l $$\chi_{3200}(801, \cdot)$$ n/a 140 2
3200.2.n $$\chi_{3200}(1407, \cdot)$$ n/a 144 2
3200.2.o $$\chi_{3200}(1343, \cdot)$$ n/a 144 2
3200.2.q $$\chi_{3200}(1249, \cdot)$$ n/a 136 2
3200.2.s $$\chi_{3200}(2143, \cdot)$$ n/a 136 2
3200.2.u $$\chi_{3200}(641, \cdot)$$ n/a 480 4
3200.2.v $$\chi_{3200}(143, \cdot)$$ n/a 280 4
3200.2.y $$\chi_{3200}(401, \cdot)$$ n/a 292 4
3200.2.ba $$\chi_{3200}(49, \cdot)$$ n/a 280 4
3200.2.bb $$\chi_{3200}(207, \cdot)$$ n/a 280 4
3200.2.be $$\chi_{3200}(1089, \cdot)$$ n/a 480 4
3200.2.bg $$\chi_{3200}(129, \cdot)$$ n/a 480 4
3200.2.bj $$\chi_{3200}(321, \cdot)$$ n/a 480 4
3200.2.bl $$\chi_{3200}(407, \cdot)$$ None 0 8
3200.2.bm $$\chi_{3200}(201, \cdot)$$ None 0 8
3200.2.bn $$\chi_{3200}(249, \cdot)$$ None 0 8
3200.2.br $$\chi_{3200}(7, \cdot)$$ None 0 8
3200.2.bt $$\chi_{3200}(223, \cdot)$$ n/a 928 8
3200.2.bu $$\chi_{3200}(161, \cdot)$$ n/a 928 8
3200.2.bx $$\chi_{3200}(63, \cdot)$$ n/a 960 8
3200.2.by $$\chi_{3200}(127, \cdot)$$ n/a 960 8
3200.2.cb $$\chi_{3200}(289, \cdot)$$ n/a 928 8
3200.2.cc $$\chi_{3200}(1183, \cdot)$$ n/a 928 8
3200.2.cf $$\chi_{3200}(107, \cdot)$$ n/a 4576 16
3200.2.cg $$\chi_{3200}(101, \cdot)$$ n/a 4816 16
3200.2.ci $$\chi_{3200}(149, \cdot)$$ n/a 4576 16
3200.2.cl $$\chi_{3200}(43, \cdot)$$ n/a 4576 16
3200.2.cn $$\chi_{3200}(47, \cdot)$$ n/a 1888 16
3200.2.co $$\chi_{3200}(209, \cdot)$$ n/a 1888 16
3200.2.cq $$\chi_{3200}(81, \cdot)$$ n/a 1888 16
3200.2.ct $$\chi_{3200}(303, \cdot)$$ n/a 1888 16
3200.2.cu $$\chi_{3200}(23, \cdot)$$ None 0 32
3200.2.cy $$\chi_{3200}(9, \cdot)$$ None 0 32
3200.2.cz $$\chi_{3200}(41, \cdot)$$ None 0 32
3200.2.da $$\chi_{3200}(87, \cdot)$$ None 0 32
3200.2.dc $$\chi_{3200}(67, \cdot)$$ n/a 30592 64
3200.2.df $$\chi_{3200}(29, \cdot)$$ n/a 30592 64
3200.2.dh $$\chi_{3200}(21, \cdot)$$ n/a 30592 64
3200.2.di $$\chi_{3200}(3, \cdot)$$ n/a 30592 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3200))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3200)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(400))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(640))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(800))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1600))$$$$^{\oplus 2}$$