## Defining parameters

 Level: $$N$$ = $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$99$$ Sturm bound: $$108000$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(950))$$.

Total New Old
Modular forms 28008 8247 19761
Cusp forms 25993 8247 17746
Eisenstein series 2015 0 2015

## Trace form

 $$8247q + 2q^{2} + 8q^{3} + 2q^{4} + 10q^{5} + 8q^{6} + 16q^{7} + 2q^{8} + 26q^{9} + O(q^{10})$$ $$8247q + 2q^{2} + 8q^{3} + 2q^{4} + 10q^{5} + 8q^{6} + 16q^{7} + 2q^{8} + 26q^{9} + 10q^{10} + 24q^{11} + 14q^{12} + 52q^{13} + 34q^{14} + 40q^{15} + 2q^{16} + 14q^{17} + 3q^{18} + 22q^{19} + 26q^{21} - 29q^{22} - 14q^{23} - 32q^{24} - 70q^{25} + 6q^{26} - 7q^{27} - 18q^{28} - 2q^{29} - 40q^{30} + 2q^{31} - 8q^{32} + 70q^{33} - 14q^{34} + 40q^{35} + 26q^{36} + 84q^{37} + 20q^{38} + 86q^{39} + 10q^{40} + 62q^{41} + 64q^{42} + 50q^{43} + 33q^{44} - 30q^{45} + 84q^{46} + 88q^{47} + 17q^{48} + 84q^{49} + 50q^{50} + 123q^{51} + 34q^{52} + 90q^{53} + 134q^{54} + 40q^{55} + 52q^{56} + 90q^{57} + 96q^{58} + 90q^{59} + 82q^{61} - 2q^{62} + 24q^{63} + 8q^{64} - 70q^{65} + 48q^{66} + 54q^{67} - 75q^{68} - 34q^{69} - 80q^{70} + 56q^{71} + 35q^{72} + 21q^{73} - 124q^{74} - 120q^{75} - 20q^{76} - 236q^{77} - 340q^{78} - 210q^{79} + 10q^{80} - 395q^{81} - 328q^{82} - 512q^{83} - 434q^{84} - 318q^{85} - 284q^{86} - 1012q^{87} + 24q^{88} - 390q^{89} - 350q^{90} - 416q^{91} - 244q^{92} - 866q^{93} - 408q^{94} - 156q^{95} + 8q^{96} - 186q^{97} - 390q^{98} - 753q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(950))$$

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
950.2.a $$\chi_{950}(1, \cdot)$$ 950.2.a.a 1 1
950.2.a.b 1
950.2.a.c 1
950.2.a.d 1
950.2.a.e 1
950.2.a.f 2
950.2.a.g 2
950.2.a.h 2
950.2.a.i 3
950.2.a.j 3
950.2.a.k 3
950.2.a.l 3
950.2.a.m 3
950.2.a.n 3
950.2.b $$\chi_{950}(799, \cdot)$$ 950.2.b.a 2 1
950.2.b.b 2
950.2.b.c 2
950.2.b.d 2
950.2.b.e 2
950.2.b.f 4
950.2.b.g 6
950.2.b.h 6
950.2.e $$\chi_{950}(201, \cdot)$$ 950.2.e.a 2 2
950.2.e.b 2
950.2.e.c 2
950.2.e.d 2
950.2.e.e 2
950.2.e.f 2
950.2.e.g 2
950.2.e.h 4
950.2.e.i 4
950.2.e.j 4
950.2.e.k 4
950.2.e.l 8
950.2.e.m 8
950.2.e.n 10
950.2.e.o 10
950.2.f $$\chi_{950}(493, \cdot)$$ 950.2.f.a 4 2
950.2.f.b 8
950.2.f.c 16
950.2.f.d 32
950.2.h $$\chi_{950}(191, \cdot)$$ 950.2.h.a 4 4
950.2.h.b 40
950.2.h.c 44
950.2.h.d 44
950.2.h.e 44
950.2.j $$\chi_{950}(49, \cdot)$$ 950.2.j.a 4 2
950.2.j.b 4
950.2.j.c 4
950.2.j.d 4
950.2.j.e 4
950.2.j.f 8
950.2.j.g 8
950.2.j.h 8
950.2.j.i 16
950.2.l $$\chi_{950}(101, \cdot)$$ 950.2.l.a 6 6
950.2.l.b 6
950.2.l.c 6
950.2.l.d 6
950.2.l.e 6
950.2.l.f 6
950.2.l.g 12
950.2.l.h 12
950.2.l.i 18
950.2.l.j 24
950.2.l.k 24
950.2.l.l 30
950.2.l.m 30
950.2.n $$\chi_{950}(39, \cdot)$$ 950.2.n.a 88 4
950.2.n.b 96
950.2.q $$\chi_{950}(107, \cdot)$$ 950.2.q.a 8 4
950.2.q.b 8
950.2.q.c 8
950.2.q.d 8
950.2.q.e 24
950.2.q.f 32
950.2.q.g 32
950.2.r $$\chi_{950}(11, \cdot)$$ 950.2.r.a 200 8
950.2.r.b 200
950.2.u $$\chi_{950}(99, \cdot)$$ 950.2.u.a 12 6
950.2.u.b 12
950.2.u.c 12
950.2.u.d 12
950.2.u.e 24
950.2.u.f 24
950.2.u.g 36
950.2.u.h 48
950.2.w $$\chi_{950}(37, \cdot)$$ 950.2.w.a 400 8
950.2.x $$\chi_{950}(159, \cdot)$$ 950.2.x.a 400 8
950.2.bb $$\chi_{950}(143, \cdot)$$ 950.2.bb.a 24 12
950.2.bb.b 48
950.2.bb.c 72
950.2.bb.d 96
950.2.bb.e 120
950.2.bc $$\chi_{950}(61, \cdot)$$ 950.2.bc.a 600 24
950.2.bc.b 600
950.2.bd $$\chi_{950}(27, \cdot)$$ 950.2.bd.a 800 16
950.2.bg $$\chi_{950}(9, \cdot)$$ 950.2.bg.a 1200 24
950.2.bi $$\chi_{950}(3, \cdot)$$ 950.2.bi.a 2400 48

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(950))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(950)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 2}$$