# Properties

 Label 2175.2 Level 2175 Weight 2 Dimension 114744 Nonzero newspaces 40 Sturm bound 672000 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$2175 = 3 \cdot 5^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$672000$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2175))$$.

Total New Old
Modular forms 171136 116960 54176
Cusp forms 164865 114744 50121
Eisenstein series 6271 2216 4055

## Trace form

 $$114744 q + 2 q^{2} - 164 q^{3} - 314 q^{4} + 12 q^{5} - 248 q^{6} - 308 q^{7} + 42 q^{8} - 156 q^{9} + O(q^{10})$$ $$114744 q + 2 q^{2} - 164 q^{3} - 314 q^{4} + 12 q^{5} - 248 q^{6} - 308 q^{7} + 42 q^{8} - 156 q^{9} - 380 q^{10} + 8 q^{11} - 144 q^{12} - 304 q^{13} + 48 q^{14} - 196 q^{15} - 522 q^{16} + 4 q^{17} - 180 q^{18} - 348 q^{19} - 72 q^{20} - 254 q^{21} - 340 q^{22} - 4 q^{23} - 200 q^{24} - 476 q^{25} + 82 q^{26} - 122 q^{27} - 312 q^{28} + 42 q^{29} - 476 q^{30} - 476 q^{31} + 78 q^{32} - 120 q^{33} - 254 q^{34} + 40 q^{35} - 228 q^{36} - 280 q^{37} + 40 q^{38} - 178 q^{39} - 452 q^{40} + 44 q^{41} - 314 q^{42} - 380 q^{43} - 68 q^{44} - 352 q^{45} - 472 q^{46} + 24 q^{47} - 204 q^{48} - 346 q^{49} - 212 q^{50} - 554 q^{51} - 336 q^{52} + 14 q^{53} - 412 q^{54} - 456 q^{55} + 196 q^{56} - 228 q^{57} - 54 q^{58} - 252 q^{60} - 368 q^{61} + 188 q^{62} - 98 q^{63} + 90 q^{64} + 116 q^{65} - 66 q^{66} - 28 q^{67} + 440 q^{68} + 82 q^{69} - 168 q^{70} + 168 q^{71} + 104 q^{72} - 66 q^{73} + 296 q^{74} + 4 q^{75} - 900 q^{76} + 192 q^{77} - 58 q^{78} - 164 q^{79} + 308 q^{80} - 284 q^{81} - 272 q^{82} + 56 q^{83} - 96 q^{84} - 524 q^{85} + 8 q^{86} - 238 q^{87} - 856 q^{88} - 144 q^{89} - 176 q^{90} - 612 q^{91} - 64 q^{92} - 374 q^{93} - 708 q^{94} - 112 q^{95} - 514 q^{96} - 582 q^{97} - 50 q^{98} - 132 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2175))$$

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
2175.2.a $$\chi_{2175}(1, \cdot)$$ 2175.2.a.a 1 1
2175.2.a.b 1
2175.2.a.c 1
2175.2.a.d 1
2175.2.a.e 1
2175.2.a.f 1
2175.2.a.g 1
2175.2.a.h 1
2175.2.a.i 1
2175.2.a.j 1
2175.2.a.k 2
2175.2.a.l 2
2175.2.a.m 2
2175.2.a.n 2
2175.2.a.o 2
2175.2.a.p 2
2175.2.a.q 2
2175.2.a.r 2
2175.2.a.s 2
2175.2.a.t 3
2175.2.a.u 3
2175.2.a.v 4
2175.2.a.w 5
2175.2.a.x 5
2175.2.a.y 5
2175.2.a.z 5
2175.2.a.ba 7
2175.2.a.bb 7
2175.2.a.bc 8
2175.2.a.bd 8
2175.2.c $$\chi_{2175}(349, \cdot)$$ 2175.2.c.a 2 1
2175.2.c.b 2
2175.2.c.c 2
2175.2.c.d 2
2175.2.c.e 2
2175.2.c.f 4
2175.2.c.g 4
2175.2.c.h 4
2175.2.c.i 4
2175.2.c.j 4
2175.2.c.k 4
2175.2.c.l 6
2175.2.c.m 6
2175.2.c.n 8
2175.2.c.o 14
2175.2.c.p 16
2175.2.d $$\chi_{2175}(376, \cdot)$$ 2175.2.d.a 2 1
2175.2.d.b 2
2175.2.d.c 2
2175.2.d.d 2
2175.2.d.e 4
2175.2.d.f 10
2175.2.d.g 10
2175.2.d.h 20
2175.2.d.i 20
2175.2.d.j 24
2175.2.f $$\chi_{2175}(724, \cdot)$$ 2175.2.f.a 4 1
2175.2.f.b 4
2175.2.f.c 10
2175.2.f.d 10
2175.2.f.e 10
2175.2.f.f 10
2175.2.f.g 20
2175.2.f.h 20
2175.2.j $$\chi_{2175}(157, \cdot)$$ n/a 180 2
2175.2.l $$\chi_{2175}(824, \cdot)$$ n/a 352 2
2175.2.m $$\chi_{2175}(407, \cdot)$$ n/a 336 2
2175.2.p $$\chi_{2175}(782, \cdot)$$ n/a 352 2
2175.2.q $$\chi_{2175}(476, \cdot)$$ n/a 368 2
2175.2.s $$\chi_{2175}(307, \cdot)$$ n/a 180 2
2175.2.u $$\chi_{2175}(436, \cdot)$$ n/a 560 4
2175.2.v $$\chi_{2175}(226, \cdot)$$ n/a 564 6
2175.2.x $$\chi_{2175}(289, \cdot)$$ n/a 608 4
2175.2.z $$\chi_{2175}(784, \cdot)$$ n/a 560 4
2175.2.bc $$\chi_{2175}(811, \cdot)$$ n/a 592 4
2175.2.bf $$\chi_{2175}(274, \cdot)$$ n/a 528 6
2175.2.bh $$\chi_{2175}(151, \cdot)$$ n/a 576 6
2175.2.bi $$\chi_{2175}(49, \cdot)$$ n/a 552 6
2175.2.bl $$\chi_{2175}(742, \cdot)$$ n/a 1200 8
2175.2.bm $$\chi_{2175}(104, \cdot)$$ n/a 2368 8
2175.2.bo $$\chi_{2175}(173, \cdot)$$ n/a 2368 8
2175.2.br $$\chi_{2175}(233, \cdot)$$ n/a 2240 8
2175.2.bt $$\chi_{2175}(41, \cdot)$$ n/a 2368 8
2175.2.bu $$\chi_{2175}(133, \cdot)$$ n/a 1200 8
2175.2.bx $$\chi_{2175}(757, \cdot)$$ n/a 1080 12
2175.2.bz $$\chi_{2175}(26, \cdot)$$ n/a 2208 12
2175.2.ca $$\chi_{2175}(332, \cdot)$$ n/a 2112 12
2175.2.cd $$\chi_{2175}(107, \cdot)$$ n/a 2112 12
2175.2.ce $$\chi_{2175}(224, \cdot)$$ n/a 2112 12
2175.2.cg $$\chi_{2175}(43, \cdot)$$ n/a 1080 12
2175.2.ci $$\chi_{2175}(16, \cdot)$$ n/a 3648 24
2175.2.cj $$\chi_{2175}(91, \cdot)$$ n/a 3552 24
2175.2.cm $$\chi_{2175}(94, \cdot)$$ n/a 3552 24
2175.2.co $$\chi_{2175}(4, \cdot)$$ n/a 3648 24
2175.2.cr $$\chi_{2175}(37, \cdot)$$ n/a 7200 48
2175.2.cs $$\chi_{2175}(11, \cdot)$$ n/a 14208 48
2175.2.cu $$\chi_{2175}(23, \cdot)$$ n/a 14208 48
2175.2.cx $$\chi_{2175}(38, \cdot)$$ n/a 14208 48
2175.2.cz $$\chi_{2175}(14, \cdot)$$ n/a 14208 48
2175.2.da $$\chi_{2175}(73, \cdot)$$ n/a 7200 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2175))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2175)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(435))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(725))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2175))$$$$^{\oplus 1}$$