## Defining parameters

 Level: $$N$$ = $$92 = 2^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$6$$ Sturm bound: $$1056$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(92))$$.

Total New Old
Modular forms 319 176 143
Cusp forms 210 132 78
Eisenstein series 109 44 65

## Trace form

 $$132 q - 11 q^{2} - 11 q^{4} - 22 q^{5} - 11 q^{6} - 11 q^{8} - 22 q^{9} + O(q^{10})$$ $$132 q - 11 q^{2} - 11 q^{4} - 22 q^{5} - 11 q^{6} - 11 q^{8} - 22 q^{9} - 11 q^{10} - 11 q^{12} - 22 q^{13} - 11 q^{14} - 11 q^{15} - 11 q^{16} - 33 q^{17} - 11 q^{18} - 11 q^{19} - 11 q^{20} - 55 q^{21} - 22 q^{23} - 22 q^{24} - 44 q^{25} - 11 q^{26} - 33 q^{27} - 11 q^{28} - 33 q^{29} - 11 q^{30} - 11 q^{31} - 11 q^{32} - 33 q^{33} + 11 q^{34} + 22 q^{35} + 44 q^{36} + 22 q^{37} + 44 q^{38} + 44 q^{39} + 77 q^{40} + 99 q^{42} + 44 q^{43} + 66 q^{44} + 66 q^{45} + 77 q^{46} + 44 q^{47} + 77 q^{48} + 44 q^{49} + 66 q^{50} + 44 q^{51} + 99 q^{52} + 77 q^{54} + 22 q^{55} + 44 q^{56} - 11 q^{57} + 44 q^{58} - 22 q^{59} + 11 q^{60} - 66 q^{61} - 11 q^{62} - 55 q^{63} - 11 q^{64} - 99 q^{65} - 44 q^{66} - 22 q^{67} - 77 q^{69} - 22 q^{70} - 55 q^{71} + 22 q^{72} - 44 q^{73} - 22 q^{74} - 55 q^{75} - 66 q^{76} + 11 q^{77} - 121 q^{78} - 22 q^{79} - 110 q^{80} + 66 q^{81} - 77 q^{82} - 11 q^{83} - 165 q^{84} + 110 q^{85} - 121 q^{86} + 66 q^{87} - 99 q^{88} + 44 q^{89} - 198 q^{90} + 44 q^{91} - 110 q^{92} + 220 q^{93} - 88 q^{94} + 33 q^{95} - 220 q^{96} + 11 q^{97} - 99 q^{98} + 11 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$

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
92.2.a $$\chi_{92}(1, \cdot)$$ 92.2.a.a 1 1
92.2.a.b 1
92.2.b $$\chi_{92}(91, \cdot)$$ 92.2.b.a 4 1
92.2.b.b 6
92.2.e $$\chi_{92}(9, \cdot)$$ 92.2.e.a 20 10
92.2.h $$\chi_{92}(7, \cdot)$$ 92.2.h.a 100 10

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(92))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(92)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 2}$$