# Properties

 Label 35.4 Level 35 Weight 4 Dimension 112 Nonzero newspaces 6 Newform subspaces 11 Sturm bound 384 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$35 = 5 \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$384$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(35))$$.

Total New Old
Modular forms 168 144 24
Cusp forms 120 112 8
Eisenstein series 48 32 16

## Trace form

 $$112 q + 2 q^{2} + 2 q^{3} - 22 q^{4} - 11 q^{5} - 68 q^{6} - 60 q^{7} + 42 q^{8} + 124 q^{9} + O(q^{10})$$ $$112 q + 2 q^{2} + 2 q^{3} - 22 q^{4} - 11 q^{5} - 68 q^{6} - 60 q^{7} + 42 q^{8} + 124 q^{9} - 22 q^{10} - 82 q^{11} - 128 q^{12} + 64 q^{13} - 30 q^{14} - 70 q^{15} - 10 q^{16} - 214 q^{17} - 154 q^{18} + 106 q^{19} + 236 q^{20} + 426 q^{21} + 256 q^{22} - 270 q^{23} - 1056 q^{24} - 941 q^{25} - 1240 q^{26} - 664 q^{27} - 822 q^{28} + 160 q^{29} + 982 q^{30} + 990 q^{31} + 2134 q^{32} + 1678 q^{33} + 2092 q^{34} + 1305 q^{35} + 3422 q^{36} + 1394 q^{37} + 1820 q^{38} + 896 q^{39} - 132 q^{40} - 2024 q^{41} - 2304 q^{42} - 1580 q^{43} - 3284 q^{44} - 2456 q^{45} - 3540 q^{46} - 46 q^{47} - 1736 q^{48} + 344 q^{49} + 986 q^{50} - 206 q^{51} + 332 q^{52} + 914 q^{53} - 3344 q^{54} - 2878 q^{55} - 3894 q^{56} - 6412 q^{57} - 6448 q^{58} - 4810 q^{59} - 2792 q^{60} + 946 q^{61} - 624 q^{62} + 2088 q^{63} + 5158 q^{64} + 2590 q^{65} + 8588 q^{66} + 6126 q^{67} + 9244 q^{68} + 11556 q^{69} + 12666 q^{70} + 5608 q^{71} + 10866 q^{72} + 6394 q^{73} + 8968 q^{74} + 2237 q^{75} + 1508 q^{76} + 270 q^{77} - 392 q^{78} - 4314 q^{79} - 6616 q^{80} - 7922 q^{81} - 8512 q^{82} - 7764 q^{83} - 15648 q^{84} - 8542 q^{85} - 12184 q^{86} - 12400 q^{87} - 17772 q^{88} - 9990 q^{89} - 12844 q^{90} - 2364 q^{91} - 8136 q^{92} + 174 q^{93} - 1952 q^{94} + 4435 q^{95} + 5924 q^{96} + 5612 q^{97} + 4258 q^{98} + 8624 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(35))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
35.4.a $$\chi_{35}(1, \cdot)$$ 35.4.a.a 1 1
35.4.a.b 2
35.4.a.c 3
35.4.b $$\chi_{35}(29, \cdot)$$ 35.4.b.a 10 1
35.4.e $$\chi_{35}(11, \cdot)$$ 35.4.e.a 2 2
35.4.e.b 4
35.4.e.c 10
35.4.f $$\chi_{35}(13, \cdot)$$ 35.4.f.a 4 2
35.4.f.b 16
35.4.j $$\chi_{35}(4, \cdot)$$ 35.4.j.a 20 2
35.4.k $$\chi_{35}(3, \cdot)$$ 35.4.k.a 40 4

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(35))$$ into lower level spaces

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