## Defining parameters

 Level: $$N$$ = $$71$$ Weight: $$k$$ = $$10$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$4200$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_1(71))$$.

Total New Old
Modular forms 1925 1923 2
Cusp forms 1855 1855 0
Eisenstein series 70 68 2

## Trace form

 $$1855 q - 35 q^{2} - 35 q^{3} - 35 q^{4} - 35 q^{5} - 35 q^{6} - 35 q^{7} - 35 q^{8} - 35 q^{9} + O(q^{10})$$ $$1855 q - 35 q^{2} - 35 q^{3} - 35 q^{4} - 35 q^{5} - 35 q^{6} - 35 q^{7} - 35 q^{8} - 35 q^{9} - 35 q^{10} - 35 q^{11} - 35 q^{12} - 35 q^{13} - 35 q^{14} - 35 q^{15} - 35 q^{16} - 35 q^{17} - 35 q^{18} - 35 q^{19} - 35 q^{20} - 35 q^{21} - 35 q^{22} - 35 q^{23} - 35 q^{24} - 35 q^{25} - 35 q^{26} - 35 q^{27} - 35 q^{28} - 35 q^{29} - 35 q^{30} - 35 q^{31} - 35 q^{32} - 35 q^{33} - 35 q^{34} - 35 q^{35} - 35 q^{36} - 35 q^{37} - 35 q^{38} - 35 q^{39} - 35 q^{40} - 35 q^{41} - 35 q^{42} - 35 q^{43} - 35 q^{44} - 35 q^{45} - 35 q^{46} - 35 q^{47} - 35 q^{48} - 35 q^{49} - 35 q^{50} - 35 q^{51} - 35 q^{52} - 35 q^{53} - 35 q^{54} - 35 q^{55} + 215129565 q^{56} + 2169919885 q^{57} + 394382205 q^{58} - 755494215 q^{59} - 4748800035 q^{60} - 431020135 q^{61} - 199989475 q^{62} + 1392291845 q^{63} + 4813383645 q^{64} + 1254049965 q^{65} + 3394831965 q^{66} + 251825525 q^{67} - 1383710755 q^{68} - 3404268735 q^{69} - 3361400070 q^{70} - 2300307485 q^{71} - 6446487110 q^{72} + 52973725 q^{73} + 2222866205 q^{74} + 5058593715 q^{75} + 4973516765 q^{76} + 4572848525 q^{77} + 5390188125 q^{78} - 206944815 q^{79} - 8108800035 q^{80} - 7109328835 q^{81} - 8218293475 q^{82} - 1534537165 q^{83} - 688414755 q^{84} + 4033924965 q^{85} + 7556880765 q^{86} + 9161171635 q^{87} - 8011010595 q^{88} - 35 q^{89} - 35 q^{90} - 35 q^{91} - 35 q^{92} - 35 q^{93} - 35 q^{94} - 35 q^{95} - 35 q^{96} - 35 q^{97} - 35 q^{98} - 35 q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_1(71))$$

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
71.10.a $$\chi_{71}(1, \cdot)$$ 71.10.a.a 23 1
71.10.a.b 30
71.10.c $$\chi_{71}(5, \cdot)$$ 71.10.c.a 212 4
71.10.d $$\chi_{71}(20, \cdot)$$ 71.10.d.a 318 6
71.10.g $$\chi_{71}(2, \cdot)$$ 71.10.g.a 1272 24