↑

Properties

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

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(2475)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2475))\)\(^{\oplus 1}\)