# Properties

 Label 196.2 Level 196 Weight 2 Dimension 610 Nonzero newspaces 8 Newform subspaces 16 Sturm bound 4704 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$196 = 2^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$16$$ Sturm bound: $$4704$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(196))$$.

Total New Old
Modular forms 1326 706 620
Cusp forms 1027 610 417
Eisenstein series 299 96 203

## Trace form

 $$610 q - 15 q^{2} + 2 q^{3} - 15 q^{4} - 24 q^{5} - 21 q^{6} + 4 q^{7} - 33 q^{8} - 34 q^{9} + O(q^{10})$$ $$610 q - 15 q^{2} + 2 q^{3} - 15 q^{4} - 24 q^{5} - 21 q^{6} + 4 q^{7} - 33 q^{8} - 34 q^{9} - 33 q^{10} - 6 q^{11} - 45 q^{12} - 50 q^{13} - 30 q^{14} - 12 q^{15} - 39 q^{16} - 24 q^{17} - 27 q^{18} - 2 q^{19} - 21 q^{20} - 47 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} - 46 q^{25} + 3 q^{26} + 20 q^{27} + 6 q^{28} - 78 q^{29} - 9 q^{30} - 14 q^{31} - 15 q^{32} - 60 q^{33} - 21 q^{34} - 15 q^{35} - 57 q^{36} - 84 q^{37} - 57 q^{38} - 45 q^{39} - 45 q^{40} - 108 q^{41} - 33 q^{42} - 26 q^{43} - 57 q^{44} - 159 q^{45} - 45 q^{46} - 60 q^{47} - 110 q^{49} - 66 q^{50} - 78 q^{51} - 21 q^{52} - 42 q^{53} + 15 q^{54} - 69 q^{55} - 30 q^{56} - 44 q^{57} - 9 q^{58} - 24 q^{59} + 3 q^{60} - 57 q^{61} - 21 q^{62} - 18 q^{63} - 57 q^{64} - 54 q^{65} - 9 q^{66} - 14 q^{67} - 21 q^{68} - 54 q^{69} - 27 q^{70} + 9 q^{72} - 104 q^{73} + 3 q^{74} + 8 q^{75} - 21 q^{76} - 63 q^{77} + 21 q^{78} - 26 q^{79} + 90 q^{80} - 28 q^{81} + 60 q^{82} + 36 q^{83} + 210 q^{84} - 54 q^{85} + 162 q^{86} + 156 q^{87} + 174 q^{88} - 36 q^{89} + 378 q^{90} + 92 q^{91} + 120 q^{92} + 184 q^{93} + 228 q^{94} + 162 q^{95} + 384 q^{96} + 124 q^{97} + 288 q^{98} + 144 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
196.2.a $$\chi_{196}(1, \cdot)$$ 196.2.a.a 1 1
196.2.a.b 1
196.2.a.c 2
196.2.d $$\chi_{196}(195, \cdot)$$ 196.2.d.a 4 1
196.2.d.b 4
196.2.d.c 8
196.2.e $$\chi_{196}(165, \cdot)$$ 196.2.e.a 2 2
196.2.e.b 4
196.2.f $$\chi_{196}(19, \cdot)$$ 196.2.f.a 4 2
196.2.f.b 4
196.2.f.c 8
196.2.f.d 16
196.2.i $$\chi_{196}(29, \cdot)$$ 196.2.i.a 24 6
196.2.j $$\chi_{196}(27, \cdot)$$ 196.2.j.a 156 6
196.2.m $$\chi_{196}(9, \cdot)$$ 196.2.m.a 60 12
196.2.p $$\chi_{196}(3, \cdot)$$ 196.2.p.a 312 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(196))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(196)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 1}$$