# Properties

 Label 195.3 Level 195 Weight 3 Dimension 1760 Nonzero newspaces 20 Newform subspaces 35 Sturm bound 8064 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$195 = 3 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$20$$ Newform subspaces: $$35$$ Sturm bound: $$8064$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(195))$$.

Total New Old
Modular forms 2880 1896 984
Cusp forms 2496 1760 736
Eisenstein series 384 136 248

## Trace form

 $$1760 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 20 q^{6} + 32 q^{7} + 120 q^{8} - 32 q^{9} + O(q^{10})$$ $$1760 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 20 q^{6} + 32 q^{7} + 120 q^{8} - 32 q^{9} - 24 q^{10} - 8 q^{11} - 56 q^{12} - 72 q^{13} - 96 q^{14} - 22 q^{15} - 296 q^{16} + 56 q^{17} + 272 q^{18} + 136 q^{19} + 168 q^{20} + 120 q^{21} + 256 q^{22} - 16 q^{23} - 108 q^{24} - 136 q^{25} - 208 q^{26} - 256 q^{27} - 592 q^{28} - 240 q^{29} - 362 q^{30} - 264 q^{31} - 688 q^{32} - 464 q^{33} - 872 q^{34} - 160 q^{35} - 544 q^{36} - 232 q^{37} + 192 q^{38} + 292 q^{39} + 440 q^{40} + 952 q^{41} + 912 q^{42} + 952 q^{43} + 840 q^{44} + 148 q^{45} + 1144 q^{46} + 128 q^{47} + 556 q^{48} + 184 q^{49} - 472 q^{50} - 296 q^{51} - 1136 q^{52} - 928 q^{53} - 812 q^{54} - 1104 q^{55} - 2232 q^{56} - 832 q^{57} - 1712 q^{58} - 1128 q^{59} - 1604 q^{60} - 2272 q^{61} - 1784 q^{62} - 1008 q^{63} - 1808 q^{64} - 332 q^{65} - 1888 q^{66} + 56 q^{67} + 928 q^{68} + 360 q^{69} + 1200 q^{70} + 880 q^{71} + 672 q^{72} + 904 q^{73} + 1848 q^{74} + 878 q^{75} + 2456 q^{76} + 1696 q^{77} + 1520 q^{78} + 784 q^{79} + 2648 q^{80} + 856 q^{81} + 912 q^{82} + 536 q^{83} + 2904 q^{84} + 504 q^{85} + 2464 q^{86} + 2204 q^{87} + 2208 q^{88} + 2112 q^{89} + 2048 q^{90} + 2336 q^{91} + 992 q^{92} + 2424 q^{93} + 1240 q^{94} + 432 q^{95} + 1232 q^{96} + 80 q^{97} + 688 q^{98} - 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(195))$$

We only show spaces with odd 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
195.3.d $$\chi_{195}(131, \cdot)$$ 195.3.d.a 32 1
195.3.e $$\chi_{195}(194, \cdot)$$ 195.3.e.a 1 1
195.3.e.b 1
195.3.e.c 1
195.3.e.d 1
195.3.e.e 8
195.3.e.f 40
195.3.f $$\chi_{195}(14, \cdot)$$ 195.3.f.a 48 1
195.3.g $$\chi_{195}(116, \cdot)$$ 195.3.g.a 4 1
195.3.g.b 32
195.3.j $$\chi_{195}(8, \cdot)$$ 195.3.j.a 2 2
195.3.j.b 2
195.3.j.c 4
195.3.j.d 96
195.3.l $$\chi_{195}(103, \cdot)$$ 195.3.l.a 56 2
195.3.p $$\chi_{195}(31, \cdot)$$ 195.3.p.a 40 2
195.3.q $$\chi_{195}(34, \cdot)$$ 195.3.q.a 56 2
195.3.r $$\chi_{195}(118, \cdot)$$ 195.3.r.a 48 2
195.3.u $$\chi_{195}(47, \cdot)$$ 195.3.u.a 2 2
195.3.u.b 2
195.3.u.c 4
195.3.u.d 96
195.3.w $$\chi_{195}(56, \cdot)$$ 195.3.w.a 76 2
195.3.x $$\chi_{195}(29, \cdot)$$ 195.3.x.a 104 2
195.3.y $$\chi_{195}(134, \cdot)$$ 195.3.y.a 104 2
195.3.z $$\chi_{195}(146, \cdot)$$ 195.3.z.a 4 2
195.3.z.b 72
195.3.bc $$\chi_{195}(137, \cdot)$$ 195.3.bc.a 208 4
195.3.be $$\chi_{195}(22, \cdot)$$ 195.3.be.a 112 4
195.3.bi $$\chi_{195}(19, \cdot)$$ 195.3.bi.a 56 4
195.3.bi.b 56
195.3.bj $$\chi_{195}(46, \cdot)$$ 195.3.bj.a 32 4
195.3.bj.b 40
195.3.bk $$\chi_{195}(43, \cdot)$$ 195.3.bk.a 112 4
195.3.bn $$\chi_{195}(2, \cdot)$$ 195.3.bn.a 208 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(195))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(195)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 2}$$