Properties

Label 2475.4
Level 2475
Weight 4
Dimension 463274
Nonzero newspaces 84
Sturm bound 1728000
Trace bound 10

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(1728000\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2475))\).

Total New Old
Modular forms 652480 466594 185886
Cusp forms 643520 463274 180246
Eisenstein series 8960 3320 5640

Trace form

\( 463274 q - 161 q^{2} - 206 q^{3} - 93 q^{4} - 198 q^{5} - 358 q^{6} - 163 q^{7} + 13 q^{8} - 46 q^{9} + O(q^{10}) \) \( 463274 q - 161 q^{2} - 206 q^{3} - 93 q^{4} - 198 q^{5} - 358 q^{6} - 163 q^{7} + 13 q^{8} - 46 q^{9} - 340 q^{10} - 161 q^{11} - 672 q^{12} - 933 q^{13} - 2082 q^{14} - 592 q^{15} - 2041 q^{16} - 721 q^{17} - 644 q^{18} + 976 q^{19} + 1500 q^{20} + 1890 q^{21} + 2520 q^{22} + 3108 q^{23} + 2322 q^{24} - 2154 q^{25} - 3422 q^{26} - 1616 q^{27} - 10322 q^{28} - 7399 q^{29} - 2576 q^{30} - 5527 q^{31} - 10096 q^{32} - 4258 q^{33} + 200 q^{34} + 464 q^{35} - 5002 q^{36} + 5913 q^{37} + 12332 q^{38} + 4714 q^{39} + 9224 q^{40} + 12583 q^{41} + 16776 q^{42} + 8240 q^{43} + 18876 q^{44} + 3944 q^{45} + 698 q^{46} + 11437 q^{47} + 19126 q^{48} - 2463 q^{49} - 6072 q^{50} + 2116 q^{51} - 18560 q^{52} - 12309 q^{53} - 12146 q^{54} - 6798 q^{55} - 42812 q^{56} - 18138 q^{57} - 27142 q^{58} - 29188 q^{59} - 28200 q^{60} - 17405 q^{61} - 40124 q^{62} - 22122 q^{63} - 12657 q^{64} - 3626 q^{65} - 9696 q^{66} + 8152 q^{67} + 24114 q^{68} + 6118 q^{69} + 36660 q^{70} + 4535 q^{71} + 16540 q^{72} + 29725 q^{73} + 35324 q^{74} + 12864 q^{75} + 35186 q^{76} + 17352 q^{77} + 11184 q^{78} + 17103 q^{79} + 30460 q^{80} + 3826 q^{81} + 30195 q^{82} + 25440 q^{83} + 19758 q^{84} + 2138 q^{85} + 38525 q^{86} + 23542 q^{87} + 696 q^{88} + 24430 q^{89} + 1712 q^{90} + 15395 q^{91} + 53088 q^{92} + 33718 q^{93} - 196 q^{94} - 820 q^{95} + 47114 q^{96} - 28828 q^{97} - 7790 q^{98} + 16083 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2475))\)

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
2475.4.a \(\chi_{2475}(1, \cdot)\) 2475.4.a.a 1 1
2475.4.a.b 1
2475.4.a.c 1
2475.4.a.d 1
2475.4.a.e 1
2475.4.a.f 1
2475.4.a.g 1
2475.4.a.h 1
2475.4.a.i 1
2475.4.a.j 1
2475.4.a.k 1
2475.4.a.l 2
2475.4.a.m 2
2475.4.a.n 2
2475.4.a.o 2
2475.4.a.p 2
2475.4.a.q 2
2475.4.a.r 2
2475.4.a.s 3
2475.4.a.t 3
2475.4.a.u 3
2475.4.a.v 3
2475.4.a.w 3
2475.4.a.x 3
2475.4.a.y 3
2475.4.a.z 3
2475.4.a.ba 3
2475.4.a.bb 4
2475.4.a.bc 4
2475.4.a.bd 4
2475.4.a.be 4
2475.4.a.bf 5
2475.4.a.bg 5
2475.4.a.bh 5
2475.4.a.bi 5
2475.4.a.bj 5
2475.4.a.bk 5
2475.4.a.bl 5
2475.4.a.bm 5
2475.4.a.bn 6
2475.4.a.bo 7
2475.4.a.bp 7
2475.4.a.bq 7
2475.4.a.br 7
2475.4.a.bs 7
2475.4.a.bt 7
2475.4.a.bu 10
2475.4.a.bv 10
2475.4.a.bw 10
2475.4.a.bx 10
2475.4.a.by 10
2475.4.a.bz 16
2475.4.a.ca 16
2475.4.c \(\chi_{2475}(199, \cdot)\) n/a 224 1
2475.4.d \(\chi_{2475}(2474, \cdot)\) n/a 216 1
2475.4.f \(\chi_{2475}(2276, \cdot)\) n/a 228 1
2475.4.i \(\chi_{2475}(826, \cdot)\) n/a 1140 2
2475.4.k \(\chi_{2475}(307, \cdot)\) n/a 536 2
2475.4.l \(\chi_{2475}(782, \cdot)\) n/a 360 2
2475.4.n \(\chi_{2475}(361, \cdot)\) n/a 1792 4
2475.4.o \(\chi_{2475}(676, \cdot)\) n/a 1128 4
2475.4.p \(\chi_{2475}(631, \cdot)\) n/a 1792 4
2475.4.q \(\chi_{2475}(181, \cdot)\) n/a 1792 4
2475.4.r \(\chi_{2475}(496, \cdot)\) n/a 1496 4
2475.4.s \(\chi_{2475}(91, \cdot)\) n/a 1792 4
2475.4.u \(\chi_{2475}(626, \cdot)\) n/a 1356 2
2475.4.w \(\chi_{2475}(824, \cdot)\) n/a 1288 2
2475.4.z \(\chi_{2475}(1024, \cdot)\) n/a 1080 2
2475.4.ba \(\chi_{2475}(1304, \cdot)\) n/a 1440 4
2475.4.bd \(\chi_{2475}(379, \cdot)\) n/a 1792 4
2475.4.bf \(\chi_{2475}(296, \cdot)\) n/a 1440 4
2475.4.bl \(\chi_{2475}(1106, \cdot)\) n/a 1440 4
2475.4.bn \(\chi_{2475}(611, \cdot)\) n/a 1440 4
2475.4.bq \(\chi_{2475}(701, \cdot)\) n/a 912 4
2475.4.br \(\chi_{2475}(116, \cdot)\) n/a 1440 4
2475.4.bt \(\chi_{2475}(694, \cdot)\) n/a 1504 4
2475.4.bw \(\chi_{2475}(134, \cdot)\) n/a 1440 4
2475.4.bz \(\chi_{2475}(809, \cdot)\) n/a 1440 4
2475.4.ca \(\chi_{2475}(899, \cdot)\) n/a 864 4
2475.4.cc \(\chi_{2475}(359, \cdot)\) n/a 1440 4
2475.4.cd \(\chi_{2475}(289, \cdot)\) n/a 1792 4
2475.4.cf \(\chi_{2475}(874, \cdot)\) n/a 1072 4
2475.4.cg \(\chi_{2475}(64, \cdot)\) n/a 1792 4
2475.4.cj \(\chi_{2475}(559, \cdot)\) n/a 1792 4
2475.4.cm \(\chi_{2475}(494, \cdot)\) n/a 1440 4
2475.4.co \(\chi_{2475}(161, \cdot)\) n/a 1440 4
2475.4.cq \(\chi_{2475}(518, \cdot)\) n/a 2160 4
2475.4.ct \(\chi_{2475}(43, \cdot)\) n/a 2576 4
2475.4.cu \(\chi_{2475}(31, \cdot)\) n/a 8608 8
2475.4.cv \(\chi_{2475}(166, \cdot)\) n/a 7200 8
2475.4.cw \(\chi_{2475}(196, \cdot)\) n/a 8608 8
2475.4.cx \(\chi_{2475}(421, \cdot)\) n/a 8608 8
2475.4.cy \(\chi_{2475}(301, \cdot)\) n/a 5424 8
2475.4.cz \(\chi_{2475}(16, \cdot)\) n/a 8608 8
2475.4.da \(\chi_{2475}(323, \cdot)\) n/a 2880 8
2475.4.dd \(\chi_{2475}(28, \cdot)\) n/a 3584 8
2475.4.de \(\chi_{2475}(127, \cdot)\) n/a 3584 8
2475.4.dk \(\chi_{2475}(188, \cdot)\) n/a 2400 8
2475.4.dl \(\chi_{2475}(368, \cdot)\) n/a 1728 8
2475.4.dm \(\chi_{2475}(53, \cdot)\) n/a 2880 8
2475.4.dn \(\chi_{2475}(152, \cdot)\) n/a 2880 8
2475.4.do \(\chi_{2475}(118, \cdot)\) n/a 2144 8
2475.4.dp \(\chi_{2475}(1063, \cdot)\) n/a 3584 8
2475.4.dq \(\chi_{2475}(172, \cdot)\) n/a 3584 8
2475.4.dr \(\chi_{2475}(208, \cdot)\) n/a 3584 8
2475.4.dx \(\chi_{2475}(278, \cdot)\) n/a 2880 8
2475.4.dy \(\chi_{2475}(41, \cdot)\) n/a 8608 8
2475.4.ec \(\chi_{2475}(164, \cdot)\) n/a 8608 8
2475.4.ed \(\chi_{2475}(169, \cdot)\) n/a 8608 8
2475.4.ef \(\chi_{2475}(4, \cdot)\) n/a 8608 8
2475.4.eg \(\chi_{2475}(49, \cdot)\) n/a 5152 8
2475.4.ej \(\chi_{2475}(229, \cdot)\) n/a 8608 8
2475.4.em \(\chi_{2475}(239, \cdot)\) n/a 8608 8
2475.4.ep \(\chi_{2475}(74, \cdot)\) n/a 5152 8
2475.4.eq \(\chi_{2475}(29, \cdot)\) n/a 8608 8
2475.4.es \(\chi_{2475}(194, \cdot)\) n/a 8608 8
2475.4.et \(\chi_{2475}(34, \cdot)\) n/a 7200 8
2475.4.ey \(\chi_{2475}(761, \cdot)\) n/a 8608 8
2475.4.ez \(\chi_{2475}(101, \cdot)\) n/a 5424 8
2475.4.fb \(\chi_{2475}(266, \cdot)\) n/a 8608 8
2475.4.fd \(\chi_{2475}(281, \cdot)\) n/a 8608 8
2475.4.fj \(\chi_{2475}(131, \cdot)\) n/a 8608 8
2475.4.fl \(\chi_{2475}(394, \cdot)\) n/a 8608 8
2475.4.fm \(\chi_{2475}(479, \cdot)\) n/a 8608 8
2475.4.fp \(\chi_{2475}(47, \cdot)\) n/a 17216 16
2475.4.fq \(\chi_{2475}(277, \cdot)\) n/a 17216 16
2475.4.fr \(\chi_{2475}(52, \cdot)\) n/a 17216 16
2475.4.fs \(\chi_{2475}(7, \cdot)\) n/a 10304 16
2475.4.ft \(\chi_{2475}(142, \cdot)\) n/a 17216 16
2475.4.gc \(\chi_{2475}(23, \cdot)\) n/a 14400 16
2475.4.gd \(\chi_{2475}(38, \cdot)\) n/a 17216 16
2475.4.ge \(\chi_{2475}(488, \cdot)\) n/a 17216 16
2475.4.gf \(\chi_{2475}(218, \cdot)\) n/a 10304 16
2475.4.gg \(\chi_{2475}(13, \cdot)\) n/a 17216 16
2475.4.gj \(\chi_{2475}(502, \cdot)\) n/a 17216 16
2475.4.gk \(\chi_{2475}(113, \cdot)\) n/a 17216 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2475))\) into lower level spaces

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