## Defining parameters

 Level: $$N$$ = $$123 = 3 \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newforms: $$13$$ Sturm bound: $$2240$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(123))$$.

Total New Old
Modular forms 640 459 181
Cusp forms 481 379 102
Eisenstein series 159 80 79

## Trace form

 $$379q - 3q^{2} - 21q^{3} - 47q^{4} - 6q^{5} - 23q^{6} - 48q^{7} - 15q^{8} - 21q^{9} + O(q^{10})$$ $$379q - 3q^{2} - 21q^{3} - 47q^{4} - 6q^{5} - 23q^{6} - 48q^{7} - 15q^{8} - 21q^{9} - 58q^{10} - 12q^{11} - 27q^{12} - 54q^{13} - 24q^{14} - 26q^{15} - 71q^{16} - 18q^{17} - 23q^{18} - 60q^{19} - 42q^{20} - 28q^{21} - 76q^{22} - 24q^{23} - 35q^{24} - 71q^{25} - 42q^{26} - 21q^{27} - 96q^{28} - 30q^{29} + 2q^{30} - 32q^{31} + 77q^{32} + 28q^{33} + 6q^{34} + 32q^{35} + 113q^{36} + 42q^{37} + 20q^{38} + 46q^{39} + 150q^{40} - q^{41} + 96q^{42} - 44q^{43} + 156q^{44} + 54q^{45} - 32q^{46} + 72q^{47} + 89q^{48} - 17q^{49} + 7q^{50} + 22q^{51} + 2q^{52} - 14q^{53} + 17q^{54} - 112q^{55} - 120q^{56} - 40q^{57} - 130q^{58} - 60q^{59} - 62q^{60} - 102q^{61} - 96q^{62} - 28q^{63} - 167q^{64} - 64q^{65} + 24q^{66} + 12q^{67} + 74q^{68} + 36q^{69} + 216q^{70} + 88q^{71} - 35q^{72} + 46q^{73} + 126q^{74} + 109q^{75} + 420q^{76} + 64q^{77} + 138q^{78} + 40q^{79} + 214q^{80} + 19q^{81} + 317q^{82} + 76q^{83} + 204q^{84} + 192q^{85} + 268q^{86} + 30q^{87} + 180q^{88} + 70q^{89} + 82q^{90} + 168q^{91} + 72q^{92} + 28q^{93} + 176q^{94} + 40q^{95} + 117q^{96} + 22q^{97} + 29q^{98} - 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(123))$$

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
123.2.a $$\chi_{123}(1, \cdot)$$ 123.2.a.a 1 1
123.2.a.b 1
123.2.a.c 2
123.2.a.d 3
123.2.d $$\chi_{123}(40, \cdot)$$ 123.2.d.a 8 1
123.2.e $$\chi_{123}(73, \cdot)$$ 123.2.e.a 12 2
123.2.g $$\chi_{123}(10, \cdot)$$ 123.2.g.a 4 4
123.2.g.b 12
123.2.g.c 16
123.2.i $$\chi_{123}(14, \cdot)$$ 123.2.i.a 48 4
123.2.j $$\chi_{123}(4, \cdot)$$ 123.2.j.a 32 4
123.2.n $$\chi_{123}(43, \cdot)$$ 123.2.n.a 48 8
123.2.o $$\chi_{123}(11, \cdot)$$ 123.2.o.a 192 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(123))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(123)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 2}$$