## Defining parameters

 Level: $$N$$ = $$198 = 2 \cdot 3^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$25$$ Sturm bound: $$4320$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(198))$$.

Total New Old
Modular forms 1240 281 959
Cusp forms 921 281 640
Eisenstein series 319 0 319

## Trace form

 $$281q + 2q^{2} + 6q^{3} + 2q^{4} - 6q^{6} + 14q^{7} - 4q^{8} - 6q^{9} + O(q^{10})$$ $$281q + 2q^{2} + 6q^{3} + 2q^{4} - 6q^{6} + 14q^{7} - 4q^{8} - 6q^{9} + 10q^{10} + 7q^{11} + 14q^{13} + 14q^{14} + 2q^{16} + 32q^{17} + 12q^{18} + 19q^{19} - 12q^{21} - 3q^{22} - 32q^{23} - 4q^{24} - 50q^{25} - 68q^{26} - 60q^{27} - 38q^{28} - 68q^{29} - 60q^{30} - 58q^{31} - 13q^{32} - 91q^{33} - 66q^{34} - 140q^{35} - 16q^{36} - 44q^{37} - 92q^{38} - 60q^{39} - 30q^{40} - 62q^{41} - 40q^{42} - 32q^{43} + q^{44} - 20q^{45} + 44q^{46} + 28q^{47} - 6q^{48} + 54q^{49} + 10q^{50} - 28q^{51} + 24q^{52} - 78q^{53} - 18q^{54} - 10q^{55} + 4q^{56} - 86q^{57} + 52q^{58} - 69q^{59} + 6q^{61} + 46q^{62} - 56q^{63} - 4q^{64} - 60q^{65} - 60q^{67} + 14q^{68} - 80q^{69} + 40q^{70} - 32q^{71} - 6q^{72} - 64q^{73} + 12q^{74} - 40q^{75} + 8q^{76} - 86q^{77} + 12q^{78} - 38q^{79} + 10q^{80} + 58q^{81} - 61q^{82} + 129q^{83} + 92q^{84} + 30q^{85} + 133q^{86} + 164q^{87} + 7q^{88} + 156q^{89} + 200q^{90} - 156q^{91} + 78q^{92} + 200q^{93} - 32q^{94} + 270q^{95} + 25q^{97} + 147q^{98} + 302q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$

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
198.2.a $$\chi_{198}(1, \cdot)$$ 198.2.a.a 1 1
198.2.a.b 1
198.2.a.c 1
198.2.a.d 1
198.2.a.e 1
198.2.b $$\chi_{198}(197, \cdot)$$ 198.2.b.a 2 1
198.2.b.b 2
198.2.e $$\chi_{198}(67, \cdot)$$ 198.2.e.a 2 2
198.2.e.b 2
198.2.e.c 4
198.2.e.d 6
198.2.e.e 6
198.2.f $$\chi_{198}(37, \cdot)$$ 198.2.f.a 4 4
198.2.f.b 4
198.2.f.c 4
198.2.f.d 4
198.2.f.e 4
198.2.i $$\chi_{198}(65, \cdot)$$ 198.2.i.a 12 2
198.2.i.b 12
198.2.l $$\chi_{198}(17, \cdot)$$ 198.2.l.a 8 4
198.2.l.b 8
198.2.m $$\chi_{198}(25, \cdot)$$ 198.2.m.a 40 8
198.2.m.b 56
198.2.n $$\chi_{198}(29, \cdot)$$ 198.2.n.a 48 8
198.2.n.b 48

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(198))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(198)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 2}$$