# Properties

 Label 35.3 Level 35 Weight 3 Dimension 70 Nonzero newspaces 6 Newform subspaces 9 Sturm bound 288 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$35 = 5 \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$9$$ Sturm bound: $$288$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(35))$$.

Total New Old
Modular forms 120 98 22
Cusp forms 72 70 2
Eisenstein series 48 28 20

## Trace form

 $$70 q - 6 q^{2} - 12 q^{3} - 22 q^{4} - 12 q^{5} - 24 q^{6} + 2 q^{7} - 18 q^{8} - 30 q^{9} + O(q^{10})$$ $$70 q - 6 q^{2} - 12 q^{3} - 22 q^{4} - 12 q^{5} - 24 q^{6} + 2 q^{7} - 18 q^{8} - 30 q^{9} - 12 q^{10} - 12 q^{11} - 12 q^{12} - 12 q^{13} - 54 q^{14} - 24 q^{15} - 2 q^{16} - 12 q^{17} + 42 q^{18} - 12 q^{19} - 12 q^{20} - 24 q^{21} - 60 q^{22} - 48 q^{23} + 180 q^{24} + 46 q^{25} + 168 q^{26} + 240 q^{27} + 346 q^{28} + 204 q^{29} + 276 q^{30} + 48 q^{31} + 42 q^{32} + 48 q^{33} - 48 q^{35} - 330 q^{36} - 44 q^{37} - 204 q^{38} - 312 q^{39} - 444 q^{40} - 192 q^{41} - 588 q^{42} - 356 q^{43} - 432 q^{44} - 408 q^{45} - 204 q^{46} - 168 q^{47} - 444 q^{48} - 110 q^{49} + 126 q^{50} - 24 q^{51} + 180 q^{52} + 420 q^{54} + 324 q^{55} + 558 q^{56} + 552 q^{57} + 720 q^{58} + 468 q^{59} + 1068 q^{60} + 552 q^{61} + 744 q^{62} + 690 q^{63} + 878 q^{64} + 276 q^{65} + 408 q^{66} + 416 q^{67} + 168 q^{68} - 192 q^{70} - 372 q^{71} - 546 q^{72} - 396 q^{73} - 900 q^{74} - 588 q^{75} - 1032 q^{76} - 672 q^{77} - 1320 q^{78} - 784 q^{79} - 1008 q^{80} - 1050 q^{81} - 1572 q^{82} - 684 q^{83} - 1020 q^{84} - 792 q^{85} - 60 q^{86} + 168 q^{87} + 336 q^{88} + 888 q^{89} + 900 q^{90} + 600 q^{91} + 1524 q^{92} + 912 q^{93} + 948 q^{94} + 852 q^{95} + 1320 q^{96} + 492 q^{97} + 1146 q^{98} + 564 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(35))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
35.3.c $$\chi_{35}(34, \cdot)$$ 35.3.c.a 1 1
35.3.c.b 1
35.3.c.c 4
35.3.d $$\chi_{35}(6, \cdot)$$ 35.3.d.a 2 1
35.3.d.b 2
35.3.g $$\chi_{35}(8, \cdot)$$ 35.3.g.a 12 2
35.3.h $$\chi_{35}(26, \cdot)$$ 35.3.h.a 12 2
35.3.i $$\chi_{35}(19, \cdot)$$ 35.3.i.a 12 2
35.3.l $$\chi_{35}(2, \cdot)$$ 35.3.l.a 24 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(35))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(35)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 1}$$