# Properties

 Label 143.4 Level 143 Weight 4 Dimension 2350 Nonzero newspaces 12 Newform subspaces 17 Sturm bound 6720 Trace bound 3

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## Defining parameters

 Level: $$N$$ = $$143 = 11 \cdot 13$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$12$$ Newform subspaces: $$17$$ Sturm bound: $$6720$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(143))$$.

Total New Old
Modular forms 2640 2550 90
Cusp forms 2400 2350 50
Eisenstein series 240 200 40

## Trace form

 $$2350 q - 38 q^{2} - 38 q^{3} - 38 q^{4} - 38 q^{5} + 62 q^{6} + 54 q^{7} + 26 q^{8} - 198 q^{9} + O(q^{10})$$ $$2350 q - 38 q^{2} - 38 q^{3} - 38 q^{4} - 38 q^{5} + 62 q^{6} + 54 q^{7} + 26 q^{8} - 198 q^{9} - 408 q^{10} - 204 q^{11} - 876 q^{12} - 351 q^{13} + 64 q^{14} + 438 q^{15} + 722 q^{16} + 640 q^{17} + 1628 q^{18} + 400 q^{19} + 124 q^{20} - 868 q^{21} - 1694 q^{22} - 344 q^{23} - 1770 q^{24} - 656 q^{25} - 1368 q^{26} - 1532 q^{27} + 400 q^{28} + 920 q^{29} + 1864 q^{30} + 1366 q^{31} + 820 q^{32} + 966 q^{33} + 1984 q^{34} - 178 q^{35} + 184 q^{36} - 684 q^{37} - 3532 q^{38} - 957 q^{39} + 256 q^{40} - 116 q^{41} + 1152 q^{42} + 2212 q^{43} + 1952 q^{44} - 2438 q^{45} - 3484 q^{46} - 1482 q^{47} - 2120 q^{48} - 3962 q^{49} - 26 q^{50} + 1552 q^{51} + 1762 q^{52} + 1978 q^{53} + 4920 q^{54} + 1752 q^{55} + 768 q^{56} + 444 q^{57} - 4500 q^{58} - 3652 q^{59} - 5764 q^{60} + 1584 q^{61} + 4 q^{62} + 5952 q^{63} + 7934 q^{64} + 7160 q^{65} + 1432 q^{66} + 36 q^{67} - 5400 q^{68} - 5944 q^{69} - 4300 q^{70} - 4866 q^{71} - 6290 q^{72} + 742 q^{73} - 2256 q^{74} + 76 q^{75} + 3244 q^{76} + 4038 q^{77} - 4220 q^{78} + 2914 q^{79} + 92 q^{80} + 1668 q^{81} - 1194 q^{82} - 7952 q^{83} - 2956 q^{84} - 7752 q^{85} + 3746 q^{86} + 732 q^{87} - 8966 q^{88} + 3452 q^{89} + 14112 q^{90} + 3985 q^{91} + 14484 q^{92} + 13758 q^{93} + 3964 q^{94} + 594 q^{95} - 3756 q^{96} - 5372 q^{97} + 1660 q^{98} - 8480 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(143))$$

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
143.4.a $$\chi_{143}(1, \cdot)$$ 143.4.a.a 4 1
143.4.a.b 6
143.4.a.c 9
143.4.a.d 11
143.4.b $$\chi_{143}(12, \cdot)$$ 143.4.b.a 36 1
143.4.e $$\chi_{143}(100, \cdot)$$ 143.4.e.a 34 2
143.4.e.b 34
143.4.g $$\chi_{143}(21, \cdot)$$ 143.4.g.a 80 2
143.4.h $$\chi_{143}(14, \cdot)$$ 143.4.h.a 68 4
143.4.h.b 76
143.4.j $$\chi_{143}(23, \cdot)$$ 143.4.j.a 72 2
143.4.n $$\chi_{143}(25, \cdot)$$ 143.4.n.a 160 4
143.4.o $$\chi_{143}(32, \cdot)$$ 143.4.o.a 160 4
143.4.q $$\chi_{143}(3, \cdot)$$ 143.4.q.a 320 8
143.4.s $$\chi_{143}(8, \cdot)$$ 143.4.s.a 320 8
143.4.u $$\chi_{143}(4, \cdot)$$ 143.4.u.a 320 8
143.4.w $$\chi_{143}(2, \cdot)$$ 143.4.w.a 640 16

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(143))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(143)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$