# Properties

 Label 175.10 Level 175 Weight 10 Dimension 9437 Nonzero newspaces 12 Sturm bound 24000 Trace bound 2

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## Defining parameters

 Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$10$$ Nonzero newspaces: $$12$$ Sturm bound: $$24000$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_1(175))$$.

Total New Old
Modular forms 10968 9641 1327
Cusp forms 10632 9437 1195
Eisenstein series 336 204 132

## Trace form

 $$9437 q - 91 q^{2} + 727 q^{3} - 3107 q^{4} + 3502 q^{5} - 14270 q^{6} + 13223 q^{7} + 491 q^{8} - 20925 q^{9} + O(q^{10})$$ $$9437 q - 91 q^{2} + 727 q^{3} - 3107 q^{4} + 3502 q^{5} - 14270 q^{6} + 13223 q^{7} + 491 q^{8} - 20925 q^{9} - 140848 q^{10} + 425037 q^{11} + 989946 q^{12} - 369660 q^{13} - 1772369 q^{14} - 326016 q^{15} + 8850009 q^{16} + 1489207 q^{17} + 261115 q^{18} - 3989431 q^{19} - 11172868 q^{20} + 3024519 q^{21} + 7795552 q^{22} + 5613351 q^{23} + 31649494 q^{24} + 5742034 q^{25} - 4749084 q^{26} - 155834 q^{27} - 939541 q^{28} - 27880830 q^{29} - 24057116 q^{30} - 13590839 q^{31} + 72985263 q^{32} + 51165855 q^{33} + 116187830 q^{34} + 41048128 q^{35} - 30286203 q^{36} - 45574371 q^{37} - 322749460 q^{38} - 268898790 q^{39} + 240206264 q^{40} + 405466 q^{41} + 412162472 q^{42} + 295782980 q^{43} - 202078832 q^{44} - 689958082 q^{45} - 629053010 q^{46} + 214201975 q^{47} + 993315378 q^{48} + 5902701 q^{49} + 592439804 q^{50} + 442829583 q^{51} + 202825200 q^{52} - 604350451 q^{53} - 1949702914 q^{54} - 549396084 q^{55} - 1366793695 q^{56} + 213461606 q^{57} + 2315216774 q^{58} + 1428657555 q^{59} + 1697794052 q^{60} + 79214197 q^{61} - 1986831444 q^{62} - 2828374391 q^{63} - 2036521239 q^{64} + 2356478474 q^{65} + 266835998 q^{66} - 243048899 q^{67} - 676883830 q^{68} + 898935022 q^{69} + 1835549662 q^{70} - 568809796 q^{71} + 1005105459 q^{72} + 126459951 q^{73} + 5857933404 q^{74} + 2598337768 q^{75} - 7189182222 q^{76} - 2589565023 q^{77} - 4599433336 q^{78} - 667739601 q^{79} - 5494678672 q^{80} + 4332036456 q^{81} + 3148391118 q^{82} - 2595306366 q^{83} - 7800065816 q^{84} + 3033016382 q^{85} + 5344866648 q^{86} + 16129498382 q^{87} + 4867662752 q^{88} - 6064502595 q^{89} - 19529978700 q^{90} + 3011859002 q^{91} + 6556513692 q^{92} + 1402371703 q^{93} - 5243796286 q^{94} - 3875382692 q^{95} - 17246665006 q^{96} + 2725042370 q^{97} - 16474642081 q^{98} - 1365247596 q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_1(175))$$

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
175.10.a $$\chi_{175}(1, \cdot)$$ 175.10.a.a 1 1
175.10.a.b 2
175.10.a.c 2
175.10.a.d 3
175.10.a.e 4
175.10.a.f 5
175.10.a.g 6
175.10.a.h 8
175.10.a.i 8
175.10.a.j 10
175.10.a.k 10
175.10.a.l 13
175.10.a.m 13
175.10.b $$\chi_{175}(99, \cdot)$$ 175.10.b.a 2 1
175.10.b.b 4
175.10.b.c 4
175.10.b.d 6
175.10.b.e 8
175.10.b.f 10
175.10.b.g 12
175.10.b.h 16
175.10.b.i 20
175.10.e $$\chi_{175}(51, \cdot)$$ n/a 222 2
175.10.f $$\chi_{175}(118, \cdot)$$ n/a 212 2
175.10.h $$\chi_{175}(36, \cdot)$$ n/a 544 4
175.10.k $$\chi_{175}(74, \cdot)$$ n/a 212 2
175.10.n $$\chi_{175}(29, \cdot)$$ n/a 536 4
175.10.o $$\chi_{175}(68, \cdot)$$ n/a 424 4
175.10.q $$\chi_{175}(11, \cdot)$$ n/a 1424 8
175.10.s $$\chi_{175}(13, \cdot)$$ n/a 1424 8
175.10.t $$\chi_{175}(4, \cdot)$$ n/a 1424 8
175.10.x $$\chi_{175}(3, \cdot)$$ n/a 2848 16

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

## Decomposition of $$S_{10}^{\mathrm{old}}(\Gamma_1(175))$$ into lower level spaces

$$S_{10}^{\mathrm{old}}(\Gamma_1(175)) \cong$$ $$S_{10}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 3}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 1}$$