# Properties

 Label 1725.2 Level 1725 Weight 2 Dimension 71856 Nonzero newspaces 24 Sturm bound 422400 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1725 = 3 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$422400$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1725))$$.

Total New Old
Modular forms 108064 73580 34484
Cusp forms 103137 71856 31281
Eisenstein series 4927 1724 3203

## Trace form

 $$71856 q + 2 q^{2} - 125 q^{3} - 236 q^{4} + 12 q^{5} - 185 q^{6} - 230 q^{7} + 42 q^{8} - 117 q^{9} + O(q^{10})$$ $$71856 q + 2 q^{2} - 125 q^{3} - 236 q^{4} + 12 q^{5} - 185 q^{6} - 230 q^{7} + 42 q^{8} - 117 q^{9} - 284 q^{10} + 8 q^{11} - 105 q^{12} - 226 q^{13} + 48 q^{14} - 148 q^{15} - 352 q^{16} + 26 q^{17} - 97 q^{18} - 248 q^{19} - 72 q^{20} - 186 q^{21} - 252 q^{22} + 28 q^{23} - 322 q^{24} - 380 q^{25} + 56 q^{26} - 92 q^{27} - 286 q^{28} - 6 q^{29} - 204 q^{30} - 384 q^{31} + 10 q^{32} - 112 q^{33} - 202 q^{34} + 40 q^{35} - 227 q^{36} - 142 q^{37} + 94 q^{38} - 123 q^{39} - 356 q^{40} + 88 q^{41} - 165 q^{42} - 214 q^{43} + 58 q^{44} - 304 q^{45} - 298 q^{46} + 56 q^{47} - 167 q^{48} - 248 q^{49} - 212 q^{50} - 443 q^{51} - 262 q^{52} - 68 q^{53} - 373 q^{54} - 360 q^{55} + 110 q^{56} - 248 q^{57} - 228 q^{58} - 12 q^{59} - 204 q^{60} - 354 q^{61} - 8 q^{62} - 142 q^{63} - 84 q^{64} + 116 q^{65} - 170 q^{66} - 62 q^{67} + 244 q^{68} - 94 q^{69} - 424 q^{70} + 112 q^{71} + 67 q^{72} - 58 q^{73} + 290 q^{74} + 52 q^{75} - 544 q^{76} + 280 q^{77} + 137 q^{78} + 2 q^{79} + 308 q^{80} - 21 q^{81} - 62 q^{82} + 144 q^{83} + 157 q^{84} - 428 q^{85} + 228 q^{86} + 17 q^{87} - 854 q^{88} - 12 q^{89} - 128 q^{90} - 288 q^{91} + 166 q^{92} - 290 q^{93} - 388 q^{94} - 200 q^{95} - 440 q^{96} - 932 q^{97} - 630 q^{98} - 157 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1725))$$

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
1725.2.a $$\chi_{1725}(1, \cdot)$$ 1725.2.a.a 1 1
1725.2.a.b 1
1725.2.a.c 1
1725.2.a.d 1
1725.2.a.e 1
1725.2.a.f 1
1725.2.a.g 1
1725.2.a.h 1
1725.2.a.i 1
1725.2.a.j 1
1725.2.a.k 1
1725.2.a.l 1
1725.2.a.m 1
1725.2.a.n 1
1725.2.a.o 1
1725.2.a.p 1
1725.2.a.q 1
1725.2.a.r 1
1725.2.a.s 1
1725.2.a.t 1
1725.2.a.u 1
1725.2.a.v 2
1725.2.a.w 2
1725.2.a.x 2
1725.2.a.y 2
1725.2.a.z 2
1725.2.a.ba 2
1725.2.a.bb 2
1725.2.a.bc 2
1725.2.a.bd 2
1725.2.a.be 2
1725.2.a.bf 3
1725.2.a.bg 3
1725.2.a.bh 3
1725.2.a.bi 3
1725.2.a.bj 3
1725.2.a.bk 7
1725.2.a.bl 7
1725.2.b $$\chi_{1725}(1174, \cdot)$$ 1725.2.b.a 2 1
1725.2.b.b 2
1725.2.b.c 2
1725.2.b.d 2
1725.2.b.e 2
1725.2.b.f 2
1725.2.b.g 2
1725.2.b.h 2
1725.2.b.i 2
1725.2.b.j 2
1725.2.b.k 2
1725.2.b.l 2
1725.2.b.m 4
1725.2.b.n 4
1725.2.b.o 4
1725.2.b.p 4
1725.2.b.q 4
1725.2.b.r 4
1725.2.b.s 4
1725.2.b.t 6
1725.2.b.u 6
1725.2.c $$\chi_{1725}(551, \cdot)$$ n/a 146 1
1725.2.h $$\chi_{1725}(1724, \cdot)$$ n/a 140 1
1725.2.i $$\chi_{1725}(668, \cdot)$$ n/a 264 2
1725.2.j $$\chi_{1725}(643, \cdot)$$ n/a 144 2
1725.2.m $$\chi_{1725}(346, \cdot)$$ n/a 432 4
1725.2.p $$\chi_{1725}(344, \cdot)$$ n/a 944 4
1725.2.q $$\chi_{1725}(206, \cdot)$$ n/a 944 4
1725.2.r $$\chi_{1725}(139, \cdot)$$ n/a 448 4
1725.2.u $$\chi_{1725}(151, \cdot)$$ n/a 760 10
1725.2.x $$\chi_{1725}(22, \cdot)$$ n/a 960 8
1725.2.y $$\chi_{1725}(47, \cdot)$$ n/a 1760 8
1725.2.z $$\chi_{1725}(74, \cdot)$$ n/a 1400 10
1725.2.be $$\chi_{1725}(176, \cdot)$$ n/a 1460 10
1725.2.bf $$\chi_{1725}(49, \cdot)$$ n/a 720 10
1725.2.bi $$\chi_{1725}(7, \cdot)$$ n/a 1440 20
1725.2.bj $$\chi_{1725}(32, \cdot)$$ n/a 2800 20
1725.2.bk $$\chi_{1725}(16, \cdot)$$ n/a 4800 40
1725.2.bn $$\chi_{1725}(4, \cdot)$$ n/a 4800 40
1725.2.bo $$\chi_{1725}(11, \cdot)$$ n/a 9440 40
1725.2.bp $$\chi_{1725}(14, \cdot)$$ n/a 9440 40
1725.2.bs $$\chi_{1725}(2, \cdot)$$ n/a 18880 80
1725.2.bt $$\chi_{1725}(28, \cdot)$$ n/a 9600 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1725))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1725)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1725))$$$$^{\oplus 1}$$