## 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

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

## 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

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