# Properties

 Label 2475.2 Level 2475 Weight 2 Dimension 153318 Nonzero newspaces 84 Sturm bound 864000 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$2475 = 3^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$864000$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2475))$$.

Total New Old
Modular forms 220480 156638 63842
Cusp forms 211521 153318 58203
Eisenstein series 8959 3320 5639

## Trace form

 $$153318 q - 163 q^{2} - 212 q^{3} - 179 q^{4} - 198 q^{5} - 340 q^{6} - 188 q^{7} - 157 q^{8} - 196 q^{9} + O(q^{10})$$ $$153318 q - 163 q^{2} - 212 q^{3} - 179 q^{4} - 198 q^{5} - 340 q^{6} - 188 q^{7} - 157 q^{8} - 196 q^{9} - 570 q^{10} - 274 q^{11} - 408 q^{12} - 148 q^{13} - 102 q^{14} - 232 q^{15} - 233 q^{16} - 122 q^{17} - 116 q^{18} - 460 q^{19} - 60 q^{20} - 276 q^{21} - 139 q^{22} - 237 q^{23} - 6 q^{24} - 114 q^{25} - 316 q^{26} - 86 q^{27} - 188 q^{28} + 28 q^{29} - 176 q^{30} - 179 q^{31} + 97 q^{32} - 154 q^{33} - 184 q^{34} - 176 q^{35} - 334 q^{36} - 377 q^{37} - 74 q^{38} - 278 q^{39} - 46 q^{40} - 352 q^{41} - 264 q^{42} - 108 q^{43} - 81 q^{44} - 616 q^{45} - 566 q^{46} - 130 q^{47} - 380 q^{48} + 132 q^{49} + 18 q^{50} - 650 q^{51} + 408 q^{52} + 108 q^{53} - 116 q^{54} - 498 q^{55} - 88 q^{56} - 36 q^{57} + 504 q^{58} + 271 q^{59} - 360 q^{60} + 12 q^{61} + 296 q^{62} - 60 q^{63} - 159 q^{64} - 286 q^{65} - 162 q^{66} - 259 q^{67} - 240 q^{68} - 140 q^{69} - 500 q^{70} - 101 q^{71} - 494 q^{72} - 638 q^{73} - 638 q^{74} - 576 q^{75} - 694 q^{76} - 354 q^{77} - 900 q^{78} - 428 q^{79} - 1090 q^{80} - 596 q^{81} - 890 q^{82} - 858 q^{83} - 1038 q^{84} - 282 q^{85} - 992 q^{86} - 656 q^{87} - 365 q^{88} - 859 q^{89} - 688 q^{90} - 688 q^{91} - 564 q^{92} - 560 q^{93} + 374 q^{94} - 20 q^{95} - 982 q^{96} + 333 q^{97} - 127 q^{98} - 420 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2475))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2475.2.a $$\chi_{2475}(1, \cdot)$$ 2475.2.a.a 1 1
2475.2.a.b 1
2475.2.a.c 1
2475.2.a.d 1
2475.2.a.e 1
2475.2.a.f 1
2475.2.a.g 1
2475.2.a.h 1
2475.2.a.i 1
2475.2.a.j 1
2475.2.a.k 1
2475.2.a.l 2
2475.2.a.m 2
2475.2.a.n 2
2475.2.a.o 2
2475.2.a.p 2
2475.2.a.q 2
2475.2.a.r 2
2475.2.a.s 2
2475.2.a.t 2
2475.2.a.u 2
2475.2.a.v 2
2475.2.a.w 2
2475.2.a.x 2
2475.2.a.y 3
2475.2.a.z 3
2475.2.a.ba 3
2475.2.a.bb 3
2475.2.a.bc 3
2475.2.a.bd 3
2475.2.a.be 3
2475.2.a.bf 4
2475.2.a.bg 4
2475.2.a.bh 4
2475.2.a.bi 4
2475.2.a.bj 4
2475.2.c $$\chi_{2475}(199, \cdot)$$ 2475.2.c.a 2 1
2475.2.c.b 2
2475.2.c.c 2
2475.2.c.d 2
2475.2.c.e 2
2475.2.c.f 2
2475.2.c.g 2
2475.2.c.h 2
2475.2.c.i 4
2475.2.c.j 4
2475.2.c.k 4
2475.2.c.l 4
2475.2.c.m 4
2475.2.c.n 4
2475.2.c.o 4
2475.2.c.p 4
2475.2.c.q 6
2475.2.c.r 6
2475.2.c.s 8
2475.2.c.t 8
2475.2.d $$\chi_{2475}(2474, \cdot)$$ 2475.2.d.a 8 1
2475.2.d.b 16
2475.2.d.c 16
2475.2.d.d 32
2475.2.f $$\chi_{2475}(2276, \cdot)$$ 2475.2.f.a 2 1
2475.2.f.b 2
2475.2.f.c 2
2475.2.f.d 2
2475.2.f.e 4
2475.2.f.f 16
2475.2.f.g 16
2475.2.f.h 16
2475.2.f.i 16
2475.2.i $$\chi_{2475}(826, \cdot)$$ n/a 380 2
2475.2.k $$\chi_{2475}(307, \cdot)$$ n/a 176 2
2475.2.l $$\chi_{2475}(782, \cdot)$$ n/a 120 2
2475.2.n $$\chi_{2475}(361, \cdot)$$ n/a 592 4
2475.2.o $$\chi_{2475}(676, \cdot)$$ n/a 368 4
2475.2.p $$\chi_{2475}(631, \cdot)$$ n/a 592 4
2475.2.q $$\chi_{2475}(181, \cdot)$$ n/a 592 4
2475.2.r $$\chi_{2475}(496, \cdot)$$ n/a 504 4
2475.2.s $$\chi_{2475}(91, \cdot)$$ n/a 592 4
2475.2.u $$\chi_{2475}(626, \cdot)$$ n/a 444 2
2475.2.w $$\chi_{2475}(824, \cdot)$$ n/a 424 2
2475.2.z $$\chi_{2475}(1024, \cdot)$$ n/a 360 2
2475.2.ba $$\chi_{2475}(1304, \cdot)$$ n/a 480 4
2475.2.bd $$\chi_{2475}(379, \cdot)$$ n/a 592 4
2475.2.bf $$\chi_{2475}(296, \cdot)$$ n/a 480 4
2475.2.bl $$\chi_{2475}(1106, \cdot)$$ n/a 480 4
2475.2.bn $$\chi_{2475}(611, \cdot)$$ n/a 480 4
2475.2.bq $$\chi_{2475}(701, \cdot)$$ n/a 304 4
2475.2.br $$\chi_{2475}(116, \cdot)$$ n/a 480 4
2475.2.bt $$\chi_{2475}(694, \cdot)$$ n/a 496 4
2475.2.bw $$\chi_{2475}(134, \cdot)$$ n/a 480 4
2475.2.bz $$\chi_{2475}(809, \cdot)$$ n/a 480 4
2475.2.ca $$\chi_{2475}(899, \cdot)$$ n/a 288 4
2475.2.cc $$\chi_{2475}(359, \cdot)$$ n/a 480 4
2475.2.cd $$\chi_{2475}(289, \cdot)$$ n/a 592 4
2475.2.cf $$\chi_{2475}(874, \cdot)$$ n/a 352 4
2475.2.cg $$\chi_{2475}(64, \cdot)$$ n/a 592 4
2475.2.cj $$\chi_{2475}(559, \cdot)$$ n/a 592 4
2475.2.cm $$\chi_{2475}(494, \cdot)$$ n/a 480 4
2475.2.co $$\chi_{2475}(161, \cdot)$$ n/a 480 4
2475.2.cq $$\chi_{2475}(518, \cdot)$$ n/a 720 4
2475.2.ct $$\chi_{2475}(43, \cdot)$$ n/a 848 4
2475.2.cu $$\chi_{2475}(31, \cdot)$$ n/a 2848 8
2475.2.cv $$\chi_{2475}(166, \cdot)$$ n/a 2400 8
2475.2.cw $$\chi_{2475}(196, \cdot)$$ n/a 2848 8
2475.2.cx $$\chi_{2475}(421, \cdot)$$ n/a 2848 8
2475.2.cy $$\chi_{2475}(301, \cdot)$$ n/a 1776 8
2475.2.cz $$\chi_{2475}(16, \cdot)$$ n/a 2848 8
2475.2.da $$\chi_{2475}(323, \cdot)$$ n/a 960 8
2475.2.dd $$\chi_{2475}(28, \cdot)$$ n/a 1184 8
2475.2.de $$\chi_{2475}(127, \cdot)$$ n/a 1184 8
2475.2.dk $$\chi_{2475}(188, \cdot)$$ n/a 800 8
2475.2.dl $$\chi_{2475}(368, \cdot)$$ n/a 576 8
2475.2.dm $$\chi_{2475}(53, \cdot)$$ n/a 960 8
2475.2.dn $$\chi_{2475}(152, \cdot)$$ n/a 960 8
2475.2.do $$\chi_{2475}(118, \cdot)$$ n/a 704 8
2475.2.dp $$\chi_{2475}(1063, \cdot)$$ n/a 1184 8
2475.2.dq $$\chi_{2475}(172, \cdot)$$ n/a 1184 8
2475.2.dr $$\chi_{2475}(208, \cdot)$$ n/a 1184 8
2475.2.dx $$\chi_{2475}(278, \cdot)$$ n/a 960 8
2475.2.dy $$\chi_{2475}(41, \cdot)$$ n/a 2848 8
2475.2.ec $$\chi_{2475}(164, \cdot)$$ n/a 2848 8
2475.2.ed $$\chi_{2475}(169, \cdot)$$ n/a 2848 8
2475.2.ef $$\chi_{2475}(4, \cdot)$$ n/a 2848 8
2475.2.eg $$\chi_{2475}(49, \cdot)$$ n/a 1696 8
2475.2.ej $$\chi_{2475}(229, \cdot)$$ n/a 2848 8
2475.2.em $$\chi_{2475}(239, \cdot)$$ n/a 2848 8
2475.2.ep $$\chi_{2475}(74, \cdot)$$ n/a 1696 8
2475.2.eq $$\chi_{2475}(29, \cdot)$$ n/a 2848 8
2475.2.es $$\chi_{2475}(194, \cdot)$$ n/a 2848 8
2475.2.et $$\chi_{2475}(34, \cdot)$$ n/a 2400 8
2475.2.ey $$\chi_{2475}(761, \cdot)$$ n/a 2848 8
2475.2.ez $$\chi_{2475}(101, \cdot)$$ n/a 1776 8
2475.2.fb $$\chi_{2475}(266, \cdot)$$ n/a 2848 8
2475.2.fd $$\chi_{2475}(281, \cdot)$$ n/a 2848 8
2475.2.fj $$\chi_{2475}(131, \cdot)$$ n/a 2848 8
2475.2.fl $$\chi_{2475}(394, \cdot)$$ n/a 2848 8
2475.2.fm $$\chi_{2475}(479, \cdot)$$ n/a 2848 8
2475.2.fp $$\chi_{2475}(47, \cdot)$$ n/a 5696 16
2475.2.fq $$\chi_{2475}(277, \cdot)$$ n/a 5696 16
2475.2.fr $$\chi_{2475}(52, \cdot)$$ n/a 5696 16
2475.2.fs $$\chi_{2475}(7, \cdot)$$ n/a 3392 16
2475.2.ft $$\chi_{2475}(142, \cdot)$$ n/a 5696 16
2475.2.gc $$\chi_{2475}(23, \cdot)$$ n/a 4800 16
2475.2.gd $$\chi_{2475}(38, \cdot)$$ n/a 5696 16
2475.2.ge $$\chi_{2475}(488, \cdot)$$ n/a 5696 16
2475.2.gf $$\chi_{2475}(218, \cdot)$$ n/a 3392 16
2475.2.gg $$\chi_{2475}(13, \cdot)$$ n/a 5696 16
2475.2.gj $$\chi_{2475}(502, \cdot)$$ n/a 5696 16
2475.2.gk $$\chi_{2475}(113, \cdot)$$ n/a 5696 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2475))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2475)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(495))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(825))$$$$^{\oplus 2}$$