## Defining parameters

 Level: $$N$$ = $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$9$$ Sturm bound: $$1176$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(98))$$.

Total New Old
Modular forms 354 95 259
Cusp forms 235 95 140
Eisenstein series 119 0 119

## Trace form

 $$95q + q^{2} - 3q^{4} - 6q^{5} - 8q^{6} - 8q^{7} + q^{8} - 15q^{9} + O(q^{10})$$ $$95q + q^{2} - 3q^{4} - 6q^{5} - 8q^{6} - 8q^{7} + q^{8} - 15q^{9} - 6q^{10} - 12q^{11} - 6q^{13} - 6q^{14} - 24q^{15} - 3q^{16} - 30q^{17} - 11q^{18} - 24q^{19} - 6q^{20} - 26q^{21} - 12q^{22} - 24q^{23} - 8q^{24} - 21q^{25} - 22q^{26} - 48q^{27} - 8q^{28} - 18q^{29} - 24q^{30} - 24q^{31} + q^{32} - 48q^{33} - 6q^{34} - 42q^{35} - 15q^{36} + 14q^{37} + 26q^{38} + 26q^{39} + 36q^{40} + 30q^{41} + 54q^{42} + 24q^{43} + 30q^{44} + 132q^{45} + 102q^{46} + 60q^{47} + 14q^{48} + 118q^{49} + 43q^{50} + 120q^{51} + 8q^{52} + 18q^{53} + 94q^{54} + 138q^{55} + 36q^{56} + 12q^{57} + 42q^{58} + 36q^{59} + 18q^{60} + 20q^{61} + 2q^{62} - 36q^{63} - 3q^{64} - 84q^{65} - 48q^{66} - 60q^{67} - 30q^{68} - 96q^{69} - 42q^{70} - 72q^{71} - 11q^{72} - 78q^{73} - 34q^{74} - 144q^{75} - 24q^{76} - 84q^{77} - 40q^{78} - 96q^{79} - 6q^{80} - 15q^{81} - 30q^{82} + 12q^{83} - 26q^{84} - 24q^{85} - 28q^{86} + 24q^{87} - 12q^{88} + 6q^{89} - 78q^{90} - 10q^{91} - 24q^{92} + 108q^{93} - 72q^{94} + 48q^{95} - 8q^{96} + 6q^{97} - 48q^{98} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$

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
98.2.a $$\chi_{98}(1, \cdot)$$ 98.2.a.a 1 1
98.2.a.b 2
98.2.c $$\chi_{98}(67, \cdot)$$ 98.2.c.a 2 2
98.2.c.b 2
98.2.c.c 4
98.2.e $$\chi_{98}(15, \cdot)$$ 98.2.e.a 18 6
98.2.e.b 18
98.2.g $$\chi_{98}(9, \cdot)$$ 98.2.g.a 24 12
98.2.g.b 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(98))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(98)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 2}$$