## Defining parameters

 Level: $$N$$ = $$46 = 2 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$264$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(46))$$.

Total New Old
Modular forms 88 21 67
Cusp forms 45 21 24
Eisenstein series 43 0 43

## Trace form

 $$21q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} + O(q^{10})$$ $$21q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} - 6q^{10} - 12q^{11} - 4q^{12} - 14q^{13} - 8q^{14} - 2q^{15} - q^{16} + 4q^{17} + 31q^{18} + 2q^{19} + 16q^{20} + 34q^{21} + 10q^{22} + 21q^{23} - 4q^{24} + 13q^{25} + 8q^{26} + 26q^{27} + 14q^{28} - 8q^{29} + 20q^{30} - 10q^{31} - q^{32} - 26q^{33} - 18q^{34} - 26q^{35} - 13q^{36} + 6q^{37} - 20q^{38} - 12q^{39} - 6q^{40} - 20q^{41} - 32q^{42} - 12q^{44} - 12q^{45} - 23q^{46} - 4q^{47} - 4q^{48} + 9q^{49} - 31q^{50} - 28q^{51} - 14q^{52} - 32q^{53} - 18q^{54} + 16q^{55} + 14q^{56} + 30q^{57} + 14q^{58} + 50q^{59} - 2q^{60} + 26q^{61} + 34q^{62} + 6q^{63} - q^{64} + 70q^{65} + 40q^{66} - 24q^{67} + 26q^{68} + 18q^{69} + 40q^{70} + 38q^{71} + 31q^{72} - 30q^{73} + 50q^{74} + 52q^{75} - 20q^{76} + 14q^{77} + 10q^{78} + 30q^{79} + 16q^{80} + 11q^{81} + 2q^{82} + 4q^{83} - 10q^{84} - 42q^{85} - 22q^{86} - 54q^{87} - 12q^{88} - 68q^{89} - 78q^{90} - 68q^{91} - 23q^{92} - 128q^{93} - 48q^{94} - 54q^{95} - 4q^{96} - 10q^{97} - 13q^{98} + 20q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$

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
46.2.a $$\chi_{46}(1, \cdot)$$ 46.2.a.a 1 1
46.2.c $$\chi_{46}(3, \cdot)$$ 46.2.c.a 10 10
46.2.c.b 10

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(46))$$ into lower level spaces

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