# Properties

 Label 197.2 Level 197 Weight 2 Dimension 1520 Nonzero newspaces 6 Newform subspaces 9 Sturm bound 6468 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$197$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$9$$ Sturm bound: $$6468$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(197))$$.

Total New Old
Modular forms 1715 1715 0
Cusp forms 1520 1520 0
Eisenstein series 195 195 0

## Trace form

 $$1520 q - 95 q^{2} - 94 q^{3} - 91 q^{4} - 92 q^{5} - 86 q^{6} - 90 q^{7} - 83 q^{8} - 85 q^{9} + O(q^{10})$$ $$1520 q - 95 q^{2} - 94 q^{3} - 91 q^{4} - 92 q^{5} - 86 q^{6} - 90 q^{7} - 83 q^{8} - 85 q^{9} - 80 q^{10} - 86 q^{11} - 70 q^{12} - 84 q^{13} - 74 q^{14} - 74 q^{15} - 67 q^{16} - 80 q^{17} - 59 q^{18} - 78 q^{19} - 56 q^{20} - 66 q^{21} - 62 q^{22} - 74 q^{23} - 38 q^{24} - 67 q^{25} - 56 q^{26} - 58 q^{27} - 42 q^{28} - 68 q^{29} - 26 q^{30} - 66 q^{31} - 35 q^{32} - 50 q^{33} - 44 q^{34} - 50 q^{35} - 7 q^{36} - 60 q^{37} - 38 q^{38} - 42 q^{39} - 8 q^{40} - 56 q^{41} - 2 q^{42} - 54 q^{43} - 14 q^{44} - 20 q^{45} - 26 q^{46} - 50 q^{47} + 26 q^{48} - 41 q^{49} - 5 q^{50} - 26 q^{51} - 44 q^{53} + 22 q^{54} - 26 q^{55} + 22 q^{56} - 18 q^{57} - 8 q^{58} - 38 q^{59} + 70 q^{60} - 36 q^{61} - 2 q^{62} + 6 q^{63} + 29 q^{64} - 14 q^{65} + 46 q^{66} - 30 q^{67} + 28 q^{68} - 2 q^{69} + 46 q^{70} - 26 q^{71} + 97 q^{72} - 24 q^{73} + 16 q^{74} + 26 q^{75} + 42 q^{76} - 2 q^{77} + 70 q^{78} - 18 q^{79} + 88 q^{80} + 23 q^{81} + 28 q^{82} - 14 q^{83} + 126 q^{84} + 10 q^{85} + 34 q^{86} + 22 q^{87} + 82 q^{88} - 8 q^{89} + 136 q^{90} + 14 q^{91} + 70 q^{92} + 30 q^{93} + 46 q^{94} + 22 q^{95} + 154 q^{96} + 73 q^{98} + 58 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(197))$$

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
197.2.a $$\chi_{197}(1, \cdot)$$ 197.2.a.a 1 1
197.2.a.b 5
197.2.a.c 10
197.2.b $$\chi_{197}(196, \cdot)$$ 197.2.b.a 16 1
197.2.d $$\chi_{197}(36, \cdot)$$ 197.2.d.a 90 6
197.2.e $$\chi_{197}(6, \cdot)$$ 197.2.e.a 6 6
197.2.e.b 90
197.2.g $$\chi_{197}(16, \cdot)$$ 197.2.g.a 630 42
197.2.h $$\chi_{197}(4, \cdot)$$ 197.2.h.a 672 42