## Defining parameters

 Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$12$$ Sturm bound: $$12000$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(175))$$.

Total New Old
Modular forms 4968 4343 625
Cusp forms 4632 4137 495
Eisenstein series 336 206 130

## Trace form

 $$4137 q - 27 q^{2} - 58 q^{3} - 51 q^{4} + 52 q^{5} + 72 q^{6} - 81 q^{7} - 19 q^{8} + 41 q^{9} + O(q^{10})$$ $$4137 q - 27 q^{2} - 58 q^{3} - 51 q^{4} + 52 q^{5} + 72 q^{6} - 81 q^{7} - 19 q^{8} + 41 q^{9} - 48 q^{10} - 352 q^{11} + 68 q^{12} + 1096 q^{13} + 583 q^{14} - 916 q^{15} - 3247 q^{16} - 2370 q^{17} + 353 q^{18} + 3226 q^{19} + 7532 q^{20} + 2136 q^{21} + 4942 q^{22} + 12 q^{23} - 5460 q^{24} - 5616 q^{25} - 9728 q^{26} - 9916 q^{27} - 325 q^{28} + 326 q^{29} + 2084 q^{30} + 12162 q^{31} + 24705 q^{32} + 15638 q^{33} + 15960 q^{34} + 2828 q^{35} - 21763 q^{36} - 26028 q^{37} - 57484 q^{38} - 50844 q^{39} - 24136 q^{40} - 18856 q^{41} + 6234 q^{42} + 35718 q^{43} + 61106 q^{44} + 59068 q^{45} + 64114 q^{46} + 56034 q^{47} + 63340 q^{48} + 1385 q^{49} - 16196 q^{50} - 28222 q^{51} - 75900 q^{52} - 69156 q^{53} - 150036 q^{54} - 65084 q^{55} - 96197 q^{56} - 96200 q^{57} - 58186 q^{58} - 26710 q^{59} - 39148 q^{60} + 65366 q^{61} + 138508 q^{62} + 150173 q^{63} + 272257 q^{64} + 116524 q^{65} + 188940 q^{66} + 108124 q^{67} + 199540 q^{68} + 79060 q^{69} + 13062 q^{70} - 50698 q^{71} - 74619 q^{72} - 89370 q^{73} - 159654 q^{74} - 108132 q^{75} - 239008 q^{76} - 156658 q^{77} - 300560 q^{78} - 176332 q^{79} - 270872 q^{80} - 85021 q^{81} - 272944 q^{82} - 136764 q^{83} - 16382 q^{84} - 31768 q^{85} + 12962 q^{86} + 68940 q^{87} + 109362 q^{88} + 136874 q^{89} + 408500 q^{90} + 116810 q^{91} + 538158 q^{92} + 382594 q^{93} + 457512 q^{94} + 194708 q^{95} + 403536 q^{96} + 200136 q^{97} + 254367 q^{98} + 159690 q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(175))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
175.5.c $$\chi_{175}(174, \cdot)$$ 175.5.c.a 2 1
175.5.c.b 4
175.5.c.c 16
175.5.c.d 24
175.5.d $$\chi_{175}(76, \cdot)$$ 175.5.d.a 1 1
175.5.d.b 2
175.5.d.c 2
175.5.d.d 2
175.5.d.e 4
175.5.d.f 8
175.5.d.g 8
175.5.d.h 8
175.5.d.i 12
175.5.g $$\chi_{175}(43, \cdot)$$ 175.5.g.a 4 2
175.5.g.b 12
175.5.g.c 24
175.5.g.d 32
175.5.i $$\chi_{175}(26, \cdot)$$ 175.5.i.a 4 2
175.5.i.b 20
175.5.i.c 22
175.5.i.d 22
175.5.i.e 28
175.5.j $$\chi_{175}(24, \cdot)$$ 175.5.j.a 8 2
175.5.j.b 40
175.5.j.c 44
175.5.l $$\chi_{175}(6, \cdot)$$ n/a 312 4
175.5.m $$\chi_{175}(34, \cdot)$$ n/a 312 4
175.5.p $$\chi_{175}(18, \cdot)$$ n/a 184 4
175.5.r $$\chi_{175}(8, \cdot)$$ n/a 480 8
175.5.u $$\chi_{175}(19, \cdot)$$ n/a 624 8
175.5.v $$\chi_{175}(31, \cdot)$$ n/a 624 8
175.5.w $$\chi_{175}(2, \cdot)$$ n/a 1248 16

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(175))$$ into lower level spaces

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