# Properties

 Label 175.4 Level 175 Weight 4 Dimension 3077 Nonzero newspaces 12 Newform subspaces 46 Sturm bound 9600 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$12$$ Newform subspaces: $$46$$ Sturm bound: $$9600$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(175))$$.

Total New Old
Modular forms 3768 3281 487
Cusp forms 3432 3077 355
Eisenstein series 336 204 132

## Trace form

 $$3077 q - 35 q^{2} - 17 q^{3} + 13 q^{4} - 38 q^{5} - 26 q^{6} + 7 q^{7} - 85 q^{8} - 153 q^{9} + O(q^{10})$$ $$3077 q - 35 q^{2} - 17 q^{3} + 13 q^{4} - 38 q^{5} - 26 q^{6} + 7 q^{7} - 85 q^{8} - 153 q^{9} + 12 q^{10} + 101 q^{11} + 90 q^{12} - 168 q^{13} - 53 q^{14} - 96 q^{15} + 289 q^{16} + 803 q^{17} + 1231 q^{18} + 465 q^{19} - 388 q^{20} - 489 q^{21} - 2016 q^{22} - 1001 q^{23} - 1202 q^{24} - 746 q^{25} + 1488 q^{26} + 118 q^{27} + 307 q^{28} - 598 q^{29} - 476 q^{30} - 927 q^{31} - 1105 q^{32} - 1629 q^{33} - 510 q^{34} - 432 q^{35} - 4227 q^{36} - 363 q^{37} + 1264 q^{38} + 2922 q^{39} + 3784 q^{40} + 2250 q^{41} + 4124 q^{42} + 2860 q^{43} + 3760 q^{44} - 1702 q^{45} + 1758 q^{46} - 2785 q^{47} - 7710 q^{48} - 1659 q^{49} - 9096 q^{50} - 5457 q^{51} - 7528 q^{52} - 3803 q^{53} - 802 q^{54} + 1516 q^{55} + 10121 q^{56} + 11126 q^{57} + 16094 q^{58} + 13435 q^{59} + 25412 q^{60} + 5901 q^{61} + 20020 q^{62} + 3049 q^{63} + 2817 q^{64} + 334 q^{65} - 14194 q^{66} - 13219 q^{67} - 24822 q^{68} - 22346 q^{69} - 16658 q^{70} - 11460 q^{71} - 40821 q^{72} - 19821 q^{73} - 32180 q^{74} - 15512 q^{75} - 14758 q^{76} - 6723 q^{77} - 10168 q^{78} + 2639 q^{79} - 6512 q^{80} + 15264 q^{81} + 33310 q^{82} + 26402 q^{83} + 45328 q^{84} + 27402 q^{85} + 40856 q^{86} + 42638 q^{87} + 61424 q^{88} + 32013 q^{89} + 29040 q^{90} + 8202 q^{91} + 23324 q^{92} - 5549 q^{93} - 14094 q^{94} - 15012 q^{95} - 21166 q^{96} - 32894 q^{97} - 25153 q^{98} - 40980 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(175))$$

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
175.4.a $$\chi_{175}(1, \cdot)$$ 175.4.a.a 1 1
175.4.a.b 1
175.4.a.c 2
175.4.a.d 2
175.4.a.e 2
175.4.a.f 3
175.4.a.g 4
175.4.a.h 4
175.4.a.i 5
175.4.a.j 5
175.4.b $$\chi_{175}(99, \cdot)$$ 175.4.b.a 2 1
175.4.b.b 2
175.4.b.c 4
175.4.b.d 4
175.4.b.e 6
175.4.b.f 8
175.4.e $$\chi_{175}(51, \cdot)$$ 175.4.e.a 2 2
175.4.e.b 2
175.4.e.c 4
175.4.e.d 10
175.4.e.e 16
175.4.e.f 16
175.4.e.g 20
175.4.f $$\chi_{175}(118, \cdot)$$ 175.4.f.a 4 2
175.4.f.b 4
175.4.f.c 4
175.4.f.d 4
175.4.f.e 4
175.4.f.f 8
175.4.f.g 16
175.4.f.h 24
175.4.h $$\chi_{175}(36, \cdot)$$ 175.4.h.a 88 4
175.4.h.b 88
175.4.k $$\chi_{175}(74, \cdot)$$ 175.4.k.a 4 2
175.4.k.b 4
175.4.k.c 8
175.4.k.d 20
175.4.k.e 32
175.4.n $$\chi_{175}(29, \cdot)$$ 175.4.n.a 184 4
175.4.o $$\chi_{175}(68, \cdot)$$ 175.4.o.a 32 4
175.4.o.b 40
175.4.o.c 64
175.4.q $$\chi_{175}(11, \cdot)$$ 175.4.q.a 464 8
175.4.s $$\chi_{175}(13, \cdot)$$ 175.4.s.a 464 8
175.4.t $$\chi_{175}(4, \cdot)$$ 175.4.t.a 464 8
175.4.x $$\chi_{175}(3, \cdot)$$ 175.4.x.a 928 16

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(175))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(175)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 1}$$