## 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

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

## 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

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