## Defining parameters

 Level: $$N$$ = $$143 = 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$19$$ Sturm bound: $$3360$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(143))$$.

Total New Old
Modular forms 960 915 45
Cusp forms 721 715 6
Eisenstein series 239 200 39

## Trace form

 $$715q - 47q^{2} - 50q^{3} - 59q^{4} - 56q^{5} - 64q^{6} - 48q^{7} - 45q^{8} - 41q^{9} + O(q^{10})$$ $$715q - 47q^{2} - 50q^{3} - 59q^{4} - 56q^{5} - 64q^{6} - 48q^{7} - 45q^{8} - 41q^{9} - 32q^{10} - 51q^{11} - 80q^{12} - 41q^{13} - 104q^{14} - 46q^{15} - 31q^{16} - 44q^{17} - 29q^{18} - 28q^{19} - 28q^{20} - 32q^{21} - 23q^{22} - 106q^{23} + 12q^{24} - 29q^{25} - 19q^{26} - 74q^{27} + 4q^{28} - 24q^{29} + 20q^{30} - 42q^{31} + 5q^{32} - 14q^{33} - 74q^{34} - 8q^{35} + 37q^{36} - 58q^{37} - 24q^{38} - 32q^{39} - 42q^{40} + 16q^{41} + 44q^{42} + 12q^{43} + 13q^{44} - 32q^{45} + 44q^{46} - 28q^{47} + 36q^{48} + 17q^{49} + 29q^{50} + 32q^{51} + 19q^{52} - 42q^{53} + 56q^{54} + 4q^{55} + 20q^{57} + 12q^{58} - 34q^{59} + 112q^{60} - 20q^{61} + 52q^{62} + 36q^{63} + 87q^{64} + 32q^{65} + 8q^{66} - 50q^{67} + 80q^{68} + 10q^{69} + 76q^{70} + 6q^{71} + 129q^{72} + 6q^{73} + 96q^{74} + 64q^{75} + 92q^{76} + 32q^{77} + 76q^{78} - 36q^{79} + 164q^{80} + 37q^{81} + 16q^{82} + 36q^{83} + 156q^{84} + 34q^{85} + 48q^{86} + 72q^{87} + 105q^{88} - 36q^{89} + 154q^{90} + 52q^{91} + 28q^{92} + 106q^{93} + 128q^{94} + 48q^{95} + 208q^{96} + 28q^{97} + 57q^{98} + 87q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$

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
143.2.a $$\chi_{143}(1, \cdot)$$ 143.2.a.a 1 1
143.2.a.b 4
143.2.a.c 6
143.2.b $$\chi_{143}(12, \cdot)$$ 143.2.b.a 12 1
143.2.e $$\chi_{143}(100, \cdot)$$ 143.2.e.a 6 2
143.2.e.b 6
143.2.e.c 12
143.2.g $$\chi_{143}(21, \cdot)$$ 143.2.g.a 24 2
143.2.h $$\chi_{143}(14, \cdot)$$ 143.2.h.a 4 4
143.2.h.b 16
143.2.h.c 28
143.2.j $$\chi_{143}(23, \cdot)$$ 143.2.j.a 4 2
143.2.j.b 16
143.2.n $$\chi_{143}(25, \cdot)$$ 143.2.n.a 48 4
143.2.o $$\chi_{143}(32, \cdot)$$ 143.2.o.a 48 4
143.2.q $$\chi_{143}(3, \cdot)$$ 143.2.q.a 96 8
143.2.s $$\chi_{143}(8, \cdot)$$ 143.2.s.a 96 8
143.2.u $$\chi_{143}(4, \cdot)$$ 143.2.u.a 96 8
143.2.w $$\chi_{143}(2, \cdot)$$ 143.2.w.a 192 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(143))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(143)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$