# Properties

 Label 195.2 Level 195 Weight 2 Dimension 851 Nonzero newspaces 20 Newform subspaces 36 Sturm bound 5376 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$195 = 3 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$36$$ Sturm bound: $$5376$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(195))$$.

Total New Old
Modular forms 1536 979 557
Cusp forms 1153 851 302
Eisenstein series 383 128 255

## Trace form

 $$851 q + 5 q^{2} - 9 q^{3} - 15 q^{4} - q^{5} - 35 q^{6} - 24 q^{7} - 27 q^{8} - 17 q^{9} + O(q^{10})$$ $$851 q + 5 q^{2} - 9 q^{3} - 15 q^{4} - q^{5} - 35 q^{6} - 24 q^{7} - 27 q^{8} - 17 q^{9} - 61 q^{10} - 4 q^{11} - 59 q^{12} - 57 q^{13} - 24 q^{14} - 27 q^{15} - 119 q^{16} - 22 q^{17} - 55 q^{18} - 92 q^{19} - 57 q^{20} - 80 q^{21} - 116 q^{22} - 24 q^{23} - 63 q^{24} - 49 q^{25} - 83 q^{26} - 93 q^{27} - 136 q^{28} - 26 q^{29} - 41 q^{30} - 88 q^{31} - 47 q^{32} - 20 q^{33} - 62 q^{34} - 16 q^{35} + 33 q^{36} + 22 q^{37} + 68 q^{38} + 31 q^{39} - 111 q^{40} - 62 q^{41} - 24 q^{42} - 116 q^{43} - 44 q^{44} - 7 q^{45} - 240 q^{46} - 64 q^{47} + 41 q^{48} - 129 q^{49} - 85 q^{50} - 74 q^{51} - 67 q^{52} - 22 q^{53} + 37 q^{54} - 4 q^{55} + 48 q^{56} - 12 q^{57} - 22 q^{58} + 44 q^{59} + 173 q^{60} - 138 q^{61} + 120 q^{62} + 112 q^{63} + 149 q^{64} + 117 q^{65} + 140 q^{66} + 84 q^{67} + 310 q^{68} + 168 q^{69} + 144 q^{70} + 136 q^{71} + 297 q^{72} + 94 q^{73} + 154 q^{74} + 113 q^{75} + 140 q^{76} + 96 q^{77} + 281 q^{78} - 16 q^{79} + 63 q^{80} + 79 q^{81} - 58 q^{82} - 12 q^{83} + 88 q^{84} - 112 q^{85} - 52 q^{86} - 34 q^{87} - 228 q^{88} - 138 q^{89} - 43 q^{90} - 264 q^{91} - 168 q^{92} - 104 q^{93} - 296 q^{94} - 156 q^{95} - 211 q^{96} - 194 q^{97} - 155 q^{98} - 148 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$

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
195.2.a $$\chi_{195}(1, \cdot)$$ 195.2.a.a 1 1
195.2.a.b 1
195.2.a.c 1
195.2.a.d 1
195.2.a.e 3
195.2.b $$\chi_{195}(181, \cdot)$$ 195.2.b.a 2 1
195.2.b.b 2
195.2.b.c 4
195.2.c $$\chi_{195}(79, \cdot)$$ 195.2.c.a 2 1
195.2.c.b 10
195.2.h $$\chi_{195}(64, \cdot)$$ 195.2.h.a 2 1
195.2.h.b 2
195.2.h.c 12
195.2.i $$\chi_{195}(16, \cdot)$$ 195.2.i.a 2 2
195.2.i.b 2
195.2.i.c 4
195.2.i.d 6
195.2.i.e 6
195.2.k $$\chi_{195}(112, \cdot)$$ 195.2.k.a 28 2
195.2.m $$\chi_{195}(53, \cdot)$$ 195.2.m.a 48 2
195.2.n $$\chi_{195}(44, \cdot)$$ 195.2.n.a 48 2
195.2.o $$\chi_{195}(86, \cdot)$$ 195.2.o.a 40 2
195.2.s $$\chi_{195}(38, \cdot)$$ 195.2.s.a 16 2
195.2.s.b 32
195.2.t $$\chi_{195}(73, \cdot)$$ 195.2.t.a 28 2
195.2.v $$\chi_{195}(4, \cdot)$$ 195.2.v.a 32 2
195.2.ba $$\chi_{195}(94, \cdot)$$ 195.2.ba.a 24 2
195.2.bb $$\chi_{195}(121, \cdot)$$ 195.2.bb.a 4 2
195.2.bb.b 8
195.2.bb.c 8
195.2.bd $$\chi_{195}(67, \cdot)$$ 195.2.bd.a 56 4
195.2.bf $$\chi_{195}(17, \cdot)$$ 195.2.bf.a 96 4
195.2.bg $$\chi_{195}(11, \cdot)$$ 195.2.bg.a 72 4
195.2.bh $$\chi_{195}(59, \cdot)$$ 195.2.bh.a 96 4
195.2.bl $$\chi_{195}(68, \cdot)$$ 195.2.bl.a 96 4
195.2.bm $$\chi_{195}(7, \cdot)$$ 195.2.bm.a 56 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(195))$$ into lower level spaces

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