## 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

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

## 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

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