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Properties

Label 1872.4
Level 1872
Weight 4
Dimension 127292
Nonzero newspaces 70
Sturm bound 774144
Trace bound 77

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Defining parameters

Level: \( N \) = \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 70 \)
Sturm bound: \(774144\)
Trace bound: \(77\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1872))\).

Total New Old
Modular forms 292992 128182 164810
Cusp forms 287616 127292 160324
Eisenstein series 5376 890 4486

Trace form

\( 127292 q - 60 q^{2} - 60 q^{3} - 80 q^{4} - 76 q^{5} - 80 q^{6} - 72 q^{7} + 24 q^{8} + 20 q^{9} + O(q^{10}) \) \( 127292 q - 60 q^{2} - 60 q^{3} - 80 q^{4} - 76 q^{5} - 80 q^{6} - 72 q^{7} + 24 q^{8} + 20 q^{9} - 48 q^{10} + 96 q^{11} - 80 q^{12} - 33 q^{13} - 384 q^{14} - 18 q^{15} + 432 q^{16} + 70 q^{17} + 200 q^{18} - 406 q^{19} - 904 q^{20} - 698 q^{21} - 904 q^{22} - 692 q^{23} - 1552 q^{24} - 1374 q^{25} - 892 q^{26} + 624 q^{27} - 1032 q^{28} + 484 q^{29} + 920 q^{30} - 276 q^{31} + 1920 q^{32} - 90 q^{33} + 1848 q^{34} + 1062 q^{35} - 1608 q^{36} + 1650 q^{37} - 2416 q^{38} + 159 q^{39} + 1384 q^{40} - 1200 q^{41} + 1280 q^{42} - 4016 q^{43} + 4360 q^{44} + 426 q^{45} + 3440 q^{46} - 6564 q^{47} + 4808 q^{48} - 956 q^{49} + 7140 q^{50} - 3980 q^{51} + 1896 q^{52} + 3424 q^{53} + 360 q^{54} + 6658 q^{55} - 5832 q^{56} - 2320 q^{57} - 4592 q^{58} + 8456 q^{59} - 15944 q^{60} - 108 q^{61} - 9528 q^{62} + 5022 q^{63} - 3368 q^{64} - 1407 q^{65} + 9664 q^{66} - 8008 q^{67} + 6808 q^{68} + 5606 q^{69} - 7008 q^{70} - 3622 q^{71} + 15824 q^{72} - 11778 q^{73} + 8120 q^{74} + 988 q^{75} - 2504 q^{76} + 10574 q^{77} + 428 q^{78} + 2210 q^{79} - 13448 q^{80} + 772 q^{81} - 7080 q^{82} + 2988 q^{83} - 19184 q^{84} + 16306 q^{85} + 1816 q^{86} + 426 q^{87} + 25992 q^{88} + 8646 q^{89} - 2384 q^{90} + 7752 q^{91} + 29032 q^{92} - 1842 q^{93} + 21664 q^{94} + 830 q^{95} + 12840 q^{96} - 11108 q^{97} + 13108 q^{98} + 3078 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1872))\)

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
1872.4.a \(\chi_{1872}(1, \cdot)\) 1872.4.a.a 1 1
1872.4.a.b 1
1872.4.a.c 1
1872.4.a.d 1
1872.4.a.e 1
1872.4.a.f 1
1872.4.a.g 1
1872.4.a.h 1
1872.4.a.i 1
1872.4.a.j 1
1872.4.a.k 1
1872.4.a.l 1
1872.4.a.m 1
1872.4.a.n 1
1872.4.a.o 1
1872.4.a.p 1
1872.4.a.q 1
1872.4.a.r 1
1872.4.a.s 2
1872.4.a.t 2
1872.4.a.u 2
1872.4.a.v 2
1872.4.a.w 2
1872.4.a.x 2
1872.4.a.y 2
1872.4.a.z 2
1872.4.a.ba 2
1872.4.a.bb 2
1872.4.a.bc 2
1872.4.a.bd 2
1872.4.a.be 2
1872.4.a.bf 2
1872.4.a.bg 2
1872.4.a.bh 2
1872.4.a.bi 2
1872.4.a.bj 3
1872.4.a.bk 3
1872.4.a.bl 3
1872.4.a.bm 3
1872.4.a.bn 4
1872.4.a.bo 4
1872.4.a.bp 4
1872.4.a.bq 4
1872.4.a.br 5
1872.4.a.bs 5
1872.4.c \(\chi_{1872}(1585, \cdot)\) n/a 104 1
1872.4.d \(\chi_{1872}(287, \cdot)\) 1872.4.d.a 12 1
1872.4.d.b 12
1872.4.d.c 24
1872.4.d.d 24
1872.4.g \(\chi_{1872}(937, \cdot)\) None 0 1
1872.4.h \(\chi_{1872}(935, \cdot)\) None 0 1
1872.4.j \(\chi_{1872}(1223, \cdot)\) None 0 1
1872.4.m \(\chi_{1872}(649, \cdot)\) None 0 1
1872.4.n \(\chi_{1872}(1871, \cdot)\) 1872.4.n.a 4 1
1872.4.n.b 4
1872.4.n.c 4
1872.4.n.d 16
1872.4.n.e 56
1872.4.q \(\chi_{1872}(625, \cdot)\) n/a 432 2
1872.4.r \(\chi_{1872}(1537, \cdot)\) n/a 500 2
1872.4.s \(\chi_{1872}(529, \cdot)\) n/a 500 2
1872.4.t \(\chi_{1872}(289, \cdot)\) n/a 208 2
1872.4.u \(\chi_{1872}(1243, \cdot)\) n/a 836 2
1872.4.x \(\chi_{1872}(125, \cdot)\) n/a 672 2
1872.4.y \(\chi_{1872}(467, \cdot)\) n/a 672 2
1872.4.ba \(\chi_{1872}(469, \cdot)\) n/a 720 2
1872.4.be \(\chi_{1872}(343, \cdot)\) None 0 2
1872.4.bf \(\chi_{1872}(1279, \cdot)\) n/a 210 2
1872.4.bi \(\chi_{1872}(161, \cdot)\) n/a 168 2
1872.4.bj \(\chi_{1872}(1097, \cdot)\) None 0 2
1872.4.bk \(\chi_{1872}(755, \cdot)\) n/a 576 2
1872.4.bm \(\chi_{1872}(181, \cdot)\) n/a 836 2
1872.4.bp \(\chi_{1872}(1061, \cdot)\) n/a 672 2
1872.4.bq \(\chi_{1872}(307, \cdot)\) n/a 836 2
1872.4.bt \(\chi_{1872}(647, \cdot)\) None 0 2
1872.4.bu \(\chi_{1872}(217, \cdot)\) None 0 2
1872.4.bx \(\chi_{1872}(575, \cdot)\) n/a 168 2
1872.4.by \(\chi_{1872}(433, \cdot)\) n/a 208 2
1872.4.ca \(\chi_{1872}(745, \cdot)\) None 0 2
1872.4.cd \(\chi_{1872}(887, \cdot)\) None 0 2
1872.4.cf \(\chi_{1872}(95, \cdot)\) n/a 504 2
1872.4.ch \(\chi_{1872}(623, \cdot)\) n/a 504 2
1872.4.cl \(\chi_{1872}(263, \cdot)\) None 0 2
1872.4.cn \(\chi_{1872}(25, \cdot)\) None 0 2
1872.4.co \(\chi_{1872}(599, \cdot)\) None 0 2
1872.4.cq \(\chi_{1872}(121, \cdot)\) None 0 2
1872.4.cu \(\chi_{1872}(959, \cdot)\) n/a 504 2
1872.4.cw \(\chi_{1872}(191, \cdot)\) n/a 504 2
1872.4.cx \(\chi_{1872}(49, \cdot)\) n/a 500 2
1872.4.cz \(\chi_{1872}(601, \cdot)\) None 0 2
1872.4.db \(\chi_{1872}(311, \cdot)\) None 0 2
1872.4.de \(\chi_{1872}(313, \cdot)\) None 0 2
1872.4.dg \(\chi_{1872}(1031, \cdot)\) None 0 2
1872.4.dh \(\chi_{1872}(673, \cdot)\) n/a 500 2
1872.4.dj \(\chi_{1872}(911, \cdot)\) n/a 432 2
1872.4.dm \(\chi_{1872}(337, \cdot)\) n/a 500 2
1872.4.do \(\chi_{1872}(815, \cdot)\) n/a 504 2
1872.4.dq \(\chi_{1872}(23, \cdot)\) None 0 2
1872.4.dr \(\chi_{1872}(1465, \cdot)\) None 0 2
1872.4.dv \(\chi_{1872}(719, \cdot)\) n/a 168 2
1872.4.dw \(\chi_{1872}(361, \cdot)\) None 0 2
1872.4.dz \(\chi_{1872}(503, \cdot)\) None 0 2
1872.4.ea \(\chi_{1872}(197, \cdot)\) n/a 1344 4
1872.4.ed \(\chi_{1872}(19, \cdot)\) n/a 1672 4
1872.4.ee \(\chi_{1872}(245, \cdot)\) n/a 4016 4
1872.4.eg \(\chi_{1872}(187, \cdot)\) n/a 4016 4
1872.4.ei \(\chi_{1872}(331, \cdot)\) n/a 4016 4
1872.4.el \(\chi_{1872}(461, \cdot)\) n/a 4016 4
1872.4.en \(\chi_{1872}(317, \cdot)\) n/a 4016 4
1872.4.ep \(\chi_{1872}(115, \cdot)\) n/a 4016 4
1872.4.eq \(\chi_{1872}(61, \cdot)\) n/a 4016 4
1872.4.es \(\chi_{1872}(491, \cdot)\) n/a 4016 4
1872.4.ev \(\chi_{1872}(131, \cdot)\) n/a 3456 4
1872.4.ey \(\chi_{1872}(829, \cdot)\) n/a 1672 4
1872.4.ez \(\chi_{1872}(205, \cdot)\) n/a 4016 4
1872.4.fc \(\chi_{1872}(35, \cdot)\) n/a 1344 4
1872.4.fd \(\chi_{1872}(347, \cdot)\) n/a 4016 4
1872.4.ff \(\chi_{1872}(493, \cdot)\) n/a 4016 4
1872.4.fg \(\chi_{1872}(31, \cdot)\) n/a 1008 4
1872.4.fh \(\chi_{1872}(151, \cdot)\) None 0 4
1872.4.fm \(\chi_{1872}(89, \cdot)\) None 0 4
1872.4.fn \(\chi_{1872}(305, \cdot)\) n/a 336 4
1872.4.fo \(\chi_{1872}(353, \cdot)\) n/a 1000 4
1872.4.fp \(\chi_{1872}(617, \cdot)\) None 0 4
1872.4.fu \(\chi_{1872}(41, \cdot)\) None 0 4
1872.4.fv \(\chi_{1872}(401, \cdot)\) n/a 1000 4
1872.4.fy \(\chi_{1872}(271, \cdot)\) n/a 420 4
1872.4.fz \(\chi_{1872}(487, \cdot)\) None 0 4
1872.4.ga \(\chi_{1872}(583, \cdot)\) None 0 4
1872.4.gb \(\chi_{1872}(175, \cdot)\) n/a 1008 4
1872.4.gg \(\chi_{1872}(799, \cdot)\) n/a 1008 4
1872.4.gh \(\chi_{1872}(7, \cdot)\) None 0 4
1872.4.gi \(\chi_{1872}(281, \cdot)\) None 0 4
1872.4.gj \(\chi_{1872}(785, \cdot)\) n/a 1000 4
1872.4.gn \(\chi_{1872}(155, \cdot)\) n/a 4016 4
1872.4.gq \(\chi_{1872}(685, \cdot)\) n/a 1672 4
1872.4.gr \(\chi_{1872}(133, \cdot)\) n/a 4016 4
1872.4.gu \(\chi_{1872}(179, \cdot)\) n/a 1344 4
1872.4.gv \(\chi_{1872}(563, \cdot)\) n/a 4016 4
1872.4.gx \(\chi_{1872}(157, \cdot)\) n/a 3456 4
1872.4.gy \(\chi_{1872}(277, \cdot)\) n/a 4016 4
1872.4.ha \(\chi_{1872}(419, \cdot)\) n/a 4016 4
1872.4.hd \(\chi_{1872}(643, \cdot)\) n/a 4016 4
1872.4.hf \(\chi_{1872}(605, \cdot)\) n/a 4016 4
1872.4.hh \(\chi_{1872}(5, \cdot)\) n/a 4016 4
1872.4.hi \(\chi_{1872}(499, \cdot)\) n/a 4016 4
1872.4.hk \(\chi_{1872}(67, \cdot)\) n/a 4016 4
1872.4.hm \(\chi_{1872}(149, \cdot)\) n/a 4016 4
1872.4.hp \(\chi_{1872}(163, \cdot)\) n/a 1672 4
1872.4.hq \(\chi_{1872}(917, \cdot)\) n/a 1344 4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1872))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1872)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 2}\)