# Properties

 Label 1950.2 Level 1950 Weight 2 Dimension 22952 Nonzero newspaces 40 Sturm bound 403200 Trace bound 19

## Defining parameters

 Level: $$N$$ = $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$403200$$ Trace bound: $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1950))$$.

Total New Old
Modular forms 103488 22952 80536
Cusp forms 98113 22952 75161
Eisenstein series 5375 0 5375

## Trace form

 $$22952 q - 6 q^{2} - 14 q^{3} - 6 q^{4} - 20 q^{5} - 14 q^{6} - 56 q^{7} - 12 q^{8} - 10 q^{9} + O(q^{10})$$ $$22952 q - 6 q^{2} - 14 q^{3} - 6 q^{4} - 20 q^{5} - 14 q^{6} - 56 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 32 q^{11} + 14 q^{12} - 58 q^{13} - 8 q^{14} + 8 q^{15} - 14 q^{16} + 38 q^{17} + 40 q^{18} + 48 q^{19} + 16 q^{20} + 36 q^{21} + 120 q^{22} + 88 q^{23} + 26 q^{24} + 172 q^{25} - 2 q^{26} - 50 q^{27} + 32 q^{28} + 46 q^{29} + 40 q^{30} + 8 q^{31} + 14 q^{32} + 52 q^{33} + 56 q^{34} + 16 q^{35} + 18 q^{36} + 42 q^{37} - 24 q^{38} + 98 q^{39} + 12 q^{40} - 18 q^{41} + 52 q^{42} + 120 q^{43} - 40 q^{44} + 140 q^{45} + 48 q^{46} + 40 q^{47} + 18 q^{48} + 118 q^{49} - 12 q^{50} + 228 q^{51} + 32 q^{52} + 360 q^{53} + 238 q^{54} + 336 q^{55} + 152 q^{56} + 456 q^{57} + 262 q^{58} + 440 q^{59} + 32 q^{60} + 142 q^{61} + 408 q^{62} + 440 q^{63} + 36 q^{64} + 310 q^{65} + 240 q^{66} + 448 q^{67} + 30 q^{68} + 264 q^{69} + 192 q^{70} + 288 q^{71} + 130 q^{72} + 276 q^{73} + 286 q^{74} - 88 q^{75} + 144 q^{76} + 240 q^{77} + 110 q^{78} + 112 q^{79} + 4 q^{80} + 174 q^{81} - 178 q^{82} - 112 q^{83} - 164 q^{84} - 68 q^{85} - 88 q^{86} - 148 q^{87} - 40 q^{88} - 128 q^{89} - 108 q^{90} - 104 q^{91} - 96 q^{92} - 280 q^{94} - 32 q^{95} + 18 q^{96} - 204 q^{97} - 198 q^{98} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1950))$$

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
1950.2.a $$\chi_{1950}(1, \cdot)$$ 1950.2.a.a 1 1
1950.2.a.b 1
1950.2.a.c 1
1950.2.a.d 1
1950.2.a.e 1
1950.2.a.f 1
1950.2.a.g 1
1950.2.a.h 1
1950.2.a.i 1
1950.2.a.j 1
1950.2.a.k 1
1950.2.a.l 1
1950.2.a.m 1
1950.2.a.n 1
1950.2.a.o 1
1950.2.a.p 1
1950.2.a.q 1
1950.2.a.r 1
1950.2.a.s 1
1950.2.a.t 1
1950.2.a.u 1
1950.2.a.v 1
1950.2.a.w 1
1950.2.a.x 1
1950.2.a.y 1
1950.2.a.z 1
1950.2.a.ba 1
1950.2.a.bb 1
1950.2.a.bc 2
1950.2.a.bd 2
1950.2.a.be 2
1950.2.a.bf 2
1950.2.a.bg 2
1950.2.b $$\chi_{1950}(1351, \cdot)$$ 1950.2.b.a 2 1
1950.2.b.b 2
1950.2.b.c 2
1950.2.b.d 2
1950.2.b.e 2
1950.2.b.f 2
1950.2.b.g 2
1950.2.b.h 4
1950.2.b.i 4
1950.2.b.j 4
1950.2.b.k 4
1950.2.b.l 6
1950.2.b.m 6
1950.2.e $$\chi_{1950}(1249, \cdot)$$ 1950.2.e.a 2 1
1950.2.e.b 2
1950.2.e.c 2
1950.2.e.d 2
1950.2.e.e 2
1950.2.e.f 2
1950.2.e.g 2
1950.2.e.h 2
1950.2.e.i 2
1950.2.e.j 2
1950.2.e.k 2
1950.2.e.l 2
1950.2.e.m 2
1950.2.e.n 2
1950.2.e.o 4
1950.2.e.p 4
1950.2.f $$\chi_{1950}(649, \cdot)$$ 1950.2.f.a 2 1
1950.2.f.b 2
1950.2.f.c 2
1950.2.f.d 2
1950.2.f.e 2
1950.2.f.f 2
1950.2.f.g 2
1950.2.f.h 2
1950.2.f.i 2
1950.2.f.j 2
1950.2.f.k 4
1950.2.f.l 4
1950.2.f.m 4
1950.2.f.n 4
1950.2.f.o 4
1950.2.f.p 4
1950.2.i $$\chi_{1950}(451, \cdot)$$ 1950.2.i.a 2 2
1950.2.i.b 2
1950.2.i.c 2
1950.2.i.d 2
1950.2.i.e 2
1950.2.i.f 2
1950.2.i.g 2
1950.2.i.h 2
1950.2.i.i 2
1950.2.i.j 2
1950.2.i.k 2
1950.2.i.l 2
1950.2.i.m 2
1950.2.i.n 2
1950.2.i.o 2
1950.2.i.p 2
1950.2.i.q 2
1950.2.i.r 2
1950.2.i.s 2
1950.2.i.t 2
1950.2.i.u 2
1950.2.i.v 2
1950.2.i.w 2
1950.2.i.x 2
1950.2.i.y 4
1950.2.i.z 4
1950.2.i.ba 4
1950.2.i.bb 4
1950.2.i.bc 4
1950.2.i.bd 4
1950.2.i.be 4
1950.2.i.bf 4
1950.2.i.bg 4
1950.2.i.bh 4
1950.2.i.bi 4
1950.2.j $$\chi_{1950}(1243, \cdot)$$ 1950.2.j.a 12 2
1950.2.j.b 12
1950.2.j.c 12
1950.2.j.d 16
1950.2.j.e 16
1950.2.j.f 16
1950.2.l $$\chi_{1950}(443, \cdot)$$ n/a 144 2
1950.2.n $$\chi_{1950}(749, \cdot)$$ n/a 168 2
1950.2.p $$\chi_{1950}(551, \cdot)$$ n/a 180 2
1950.2.s $$\chi_{1950}(857, \cdot)$$ n/a 168 2
1950.2.t $$\chi_{1950}(307, \cdot)$$ 1950.2.t.a 12 2
1950.2.t.b 12
1950.2.t.c 12
1950.2.t.d 16
1950.2.t.e 16
1950.2.t.f 16
1950.2.v $$\chi_{1950}(391, \cdot)$$ n/a 240 4
1950.2.y $$\chi_{1950}(49, \cdot)$$ 1950.2.y.a 4 2
1950.2.y.b 4
1950.2.y.c 4
1950.2.y.d 4
1950.2.y.e 4
1950.2.y.f 4
1950.2.y.g 4
1950.2.y.h 4
1950.2.y.i 8
1950.2.y.j 8
1950.2.y.k 8
1950.2.y.l 8
1950.2.y.m 12
1950.2.y.n 12
1950.2.z $$\chi_{1950}(1699, \cdot)$$ 1950.2.z.a 4 2
1950.2.z.b 4
1950.2.z.c 4
1950.2.z.d 4
1950.2.z.e 4
1950.2.z.f 4
1950.2.z.g 4
1950.2.z.h 4
1950.2.z.i 4
1950.2.z.j 4
1950.2.z.k 4
1950.2.z.l 4
1950.2.z.m 8
1950.2.z.n 8
1950.2.z.o 8
1950.2.z.p 8
1950.2.bc $$\chi_{1950}(751, \cdot)$$ 1950.2.bc.a 4 2
1950.2.bc.b 4
1950.2.bc.c 4
1950.2.bc.d 4
1950.2.bc.e 8
1950.2.bc.f 8
1950.2.bc.g 8
1950.2.bc.h 12
1950.2.bc.i 12
1950.2.bc.j 12
1950.2.bc.k 12
1950.2.bd $$\chi_{1950}(79, \cdot)$$ n/a 240 4
1950.2.bg $$\chi_{1950}(181, \cdot)$$ n/a 288 4
1950.2.bj $$\chi_{1950}(259, \cdot)$$ n/a 272 4
1950.2.bl $$\chi_{1950}(7, \cdot)$$ n/a 168 4
1950.2.bm $$\chi_{1950}(257, \cdot)$$ n/a 336 4
1950.2.bp $$\chi_{1950}(401, \cdot)$$ n/a 352 4
1950.2.br $$\chi_{1950}(149, \cdot)$$ n/a 336 4
1950.2.bt $$\chi_{1950}(107, \cdot)$$ n/a 336 4
1950.2.bv $$\chi_{1950}(193, \cdot)$$ n/a 168 4
1950.2.bw $$\chi_{1950}(61, \cdot)$$ n/a 544 8
1950.2.by $$\chi_{1950}(73, \cdot)$$ n/a 560 8
1950.2.bz $$\chi_{1950}(77, \cdot)$$ n/a 1120 8
1950.2.cc $$\chi_{1950}(161, \cdot)$$ n/a 1120 8
1950.2.ce $$\chi_{1950}(239, \cdot)$$ n/a 1120 8
1950.2.cg $$\chi_{1950}(53, \cdot)$$ n/a 960 8
1950.2.ci $$\chi_{1950}(697, \cdot)$$ n/a 560 8
1950.2.cj $$\chi_{1950}(439, \cdot)$$ n/a 544 8
1950.2.cm $$\chi_{1950}(121, \cdot)$$ n/a 576 8
1950.2.cp $$\chi_{1950}(139, \cdot)$$ n/a 576 8
1950.2.cq $$\chi_{1950}(37, \cdot)$$ n/a 1120 16
1950.2.cs $$\chi_{1950}(113, \cdot)$$ n/a 2240 16
1950.2.cu $$\chi_{1950}(59, \cdot)$$ n/a 2240 16
1950.2.cw $$\chi_{1950}(11, \cdot)$$ n/a 2240 16
1950.2.cz $$\chi_{1950}(17, \cdot)$$ n/a 2240 16
1950.2.da $$\chi_{1950}(67, \cdot)$$ n/a 1120 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1950))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1950)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(650))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(975))$$$$^{\oplus 2}$$