# Properties

 Label 175.7 Level 175 Weight 7 Dimension 6257 Nonzero newspaces 12 Sturm bound 16800 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$12$$ Sturm bound: $$16800$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(175))$$.

Total New Old
Modular forms 7368 6463 905
Cusp forms 7032 6257 775
Eisenstein series 336 206 130

## Trace form

 $$6257 q - 59 q^{2} + 101 q^{3} - 19 q^{4} - 168 q^{5} - 2232 q^{6} + 591 q^{7} + 6677 q^{8} - 1867 q^{9} + O(q^{10})$$ $$6257 q - 59 q^{2} + 101 q^{3} - 19 q^{4} - 168 q^{5} - 2232 q^{6} + 591 q^{7} + 6677 q^{8} - 1867 q^{9} - 8768 q^{10} - 119 q^{11} + 19868 q^{12} + 7824 q^{13} - 11177 q^{14} - 256 q^{15} - 45919 q^{16} + 4053 q^{17} + 127913 q^{18} + 68369 q^{19} - 8628 q^{20} - 68793 q^{21} - 348602 q^{22} - 220771 q^{23} - 69468 q^{24} + 131044 q^{25} + 544504 q^{26} + 713360 q^{27} + 383483 q^{28} - 35490 q^{29} - 555196 q^{30} - 659983 q^{31} - 1566439 q^{32} - 635047 q^{33} - 66040 q^{34} + 253648 q^{35} + 1610117 q^{36} + 905505 q^{37} + 1377548 q^{38} + 1419012 q^{39} + 1364024 q^{40} - 620424 q^{41} - 1051278 q^{42} - 1167090 q^{43} - 3232734 q^{44} - 2473592 q^{45} - 551470 q^{46} - 281287 q^{47} - 925652 q^{48} + 328509 q^{49} + 907404 q^{50} + 1595177 q^{51} + 2751956 q^{52} + 1848841 q^{53} + 4000644 q^{54} + 649116 q^{55} + 1177387 q^{56} + 2107582 q^{57} + 1757222 q^{58} - 2321595 q^{59} - 6869068 q^{60} - 659287 q^{61} - 2540308 q^{62} - 2986513 q^{63} + 608129 q^{64} + 166604 q^{65} - 9624444 q^{66} - 5247891 q^{67} - 7430940 q^{68} - 5605640 q^{69} - 889898 q^{70} + 3004750 q^{71} + 8086341 q^{72} + 9423393 q^{73} + 12915738 q^{74} + 6026928 q^{75} + 6543328 q^{76} + 5880891 q^{77} + 11041024 q^{78} - 511387 q^{79} + 7211208 q^{80} - 12184804 q^{81} - 16008440 q^{82} - 7028472 q^{83} - 12416078 q^{84} + 6949192 q^{85} + 187498 q^{86} + 4011198 q^{87} + 4153298 q^{88} + 1478261 q^{89} + 3942020 q^{90} + 9164470 q^{91} + 16673550 q^{92} + 1391593 q^{93} - 26052592 q^{94} - 14243052 q^{95} - 34535616 q^{96} - 26893584 q^{97} - 34333753 q^{98} - 18304854 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(175))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
175.7.c $$\chi_{175}(174, \cdot)$$ 175.7.c.a 2 1
175.7.c.b 4
175.7.c.c 4
175.7.c.d 28
175.7.c.e 32
175.7.d $$\chi_{175}(76, \cdot)$$ 175.7.d.a 1 1
175.7.d.b 2
175.7.d.c 2
175.7.d.d 2
175.7.d.e 2
175.7.d.f 14
175.7.d.g 14
175.7.d.h 16
175.7.d.i 20
175.7.g $$\chi_{175}(43, \cdot)$$ n/a 108 2
175.7.i $$\chi_{175}(26, \cdot)$$ n/a 146 2
175.7.j $$\chi_{175}(24, \cdot)$$ n/a 140 2
175.7.l $$\chi_{175}(6, \cdot)$$ n/a 472 4
175.7.m $$\chi_{175}(34, \cdot)$$ n/a 472 4
175.7.p $$\chi_{175}(18, \cdot)$$ n/a 280 4
175.7.r $$\chi_{175}(8, \cdot)$$ n/a 720 8
175.7.u $$\chi_{175}(19, \cdot)$$ n/a 944 8
175.7.v $$\chi_{175}(31, \cdot)$$ n/a 944 8
175.7.w $$\chi_{175}(2, \cdot)$$ n/a 1888 16

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

## Decomposition of $$S_{7}^{\mathrm{old}}(\Gamma_1(175))$$ into lower level spaces

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