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Properties

Label 1872.2
Level 1872
Weight 2
Dimension 42134
Nonzero newspaces 70
Sturm bound 387072
Trace bound 77

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Defining parameters

Level: \( N \) = \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 70 \)
Sturm bound: \(387072\)
Trace bound: \(77\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1872))\).

Total New Old
Modular forms 99456 43024 56432
Cusp forms 94081 42134 51947
Eisenstein series 5375 890 4485

Trace form

\( 42134 q - 60 q^{2} - 60 q^{3} - 64 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 72 q^{8} - 28 q^{9} + O(q^{10}) \) \( 42134 q - 60 q^{2} - 60 q^{3} - 64 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 72 q^{8} - 28 q^{9} - 184 q^{10} - 72 q^{11} - 80 q^{12} - 91 q^{13} - 96 q^{14} - 66 q^{15} - 16 q^{16} - 118 q^{17} - 40 q^{18} - 142 q^{19} + 40 q^{20} - 74 q^{21} + 32 q^{22} - 4 q^{23} - 16 q^{24} + 32 q^{25} - 8 q^{26} - 96 q^{27} - 104 q^{28} - 16 q^{29} - 40 q^{30} - 20 q^{31} - 138 q^{33} - 40 q^{34} + 102 q^{35} - 72 q^{36} - 242 q^{37} - 152 q^{38} - 9 q^{39} - 248 q^{40} - 12 q^{41} - 160 q^{42} + 24 q^{43} - 232 q^{44} - 54 q^{45} - 304 q^{46} + 60 q^{47} - 184 q^{48} - 250 q^{49} - 228 q^{50} + 4 q^{51} - 128 q^{52} - 196 q^{53} - 168 q^{54} - 78 q^{55} - 264 q^{56} - 64 q^{57} - 136 q^{58} - 32 q^{59} - 296 q^{60} - 88 q^{61} - 264 q^{62} - 66 q^{63} - 40 q^{64} - 267 q^{65} - 416 q^{66} - 80 q^{67} - 232 q^{68} - 250 q^{69} + 16 q^{70} - 182 q^{71} - 304 q^{72} - 14 q^{73} - 176 q^{74} - 164 q^{75} + 8 q^{76} - 146 q^{77} - 196 q^{78} - 190 q^{79} - 328 q^{80} - 332 q^{81} - 200 q^{82} - 252 q^{83} - 368 q^{84} + 10 q^{85} - 256 q^{86} - 198 q^{87} - 88 q^{88} + 42 q^{89} - 368 q^{90} - 184 q^{91} - 184 q^{92} - 18 q^{93} - 64 q^{94} - 194 q^{95} - 216 q^{96} - 16 q^{97} - 28 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1872))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1872.2.a \(\chi_{1872}(1, \cdot)\) 1872.2.a.a 1 1
1872.2.a.b 1
1872.2.a.c 1
1872.2.a.d 1
1872.2.a.e 1
1872.2.a.f 1
1872.2.a.g 1
1872.2.a.h 1
1872.2.a.i 1
1872.2.a.j 1
1872.2.a.k 1
1872.2.a.l 1
1872.2.a.m 1
1872.2.a.n 1
1872.2.a.o 1
1872.2.a.p 1
1872.2.a.q 1
1872.2.a.r 1
1872.2.a.s 1
1872.2.a.t 1
1872.2.a.u 2
1872.2.a.v 2
1872.2.a.w 2
1872.2.a.x 2
1872.2.a.y 2
1872.2.c \(\chi_{1872}(1585, \cdot)\) 1872.2.c.a 2 1
1872.2.c.b 2
1872.2.c.c 2
1872.2.c.d 2
1872.2.c.e 2
1872.2.c.f 2
1872.2.c.g 2
1872.2.c.h 2
1872.2.c.i 2
1872.2.c.j 4
1872.2.c.k 4
1872.2.c.l 8
1872.2.d \(\chi_{1872}(287, \cdot)\) 1872.2.d.a 4 1
1872.2.d.b 4
1872.2.d.c 8
1872.2.d.d 8
1872.2.g \(\chi_{1872}(937, \cdot)\) None 0 1
1872.2.h \(\chi_{1872}(935, \cdot)\) None 0 1
1872.2.j \(\chi_{1872}(1223, \cdot)\) None 0 1
1872.2.m \(\chi_{1872}(649, \cdot)\) None 0 1
1872.2.n \(\chi_{1872}(1871, \cdot)\) 1872.2.n.a 4 1
1872.2.n.b 4
1872.2.n.c 4
1872.2.n.d 8
1872.2.n.e 8
1872.2.q \(\chi_{1872}(625, \cdot)\) n/a 144 2
1872.2.r \(\chi_{1872}(1537, \cdot)\) n/a 164 2
1872.2.s \(\chi_{1872}(529, \cdot)\) n/a 164 2
1872.2.t \(\chi_{1872}(289, \cdot)\) 1872.2.t.a 2 2
1872.2.t.b 2
1872.2.t.c 2
1872.2.t.d 2
1872.2.t.e 2
1872.2.t.f 2
1872.2.t.g 2
1872.2.t.h 2
1872.2.t.i 2
1872.2.t.j 2
1872.2.t.k 2
1872.2.t.l 2
1872.2.t.m 2
1872.2.t.n 4
1872.2.t.o 4
1872.2.t.p 4
1872.2.t.q 4
1872.2.t.r 4
1872.2.t.s 4
1872.2.t.t 6
1872.2.t.u 6
1872.2.t.v 6
1872.2.u \(\chi_{1872}(1243, \cdot)\) n/a 276 2
1872.2.x \(\chi_{1872}(125, \cdot)\) n/a 224 2
1872.2.y \(\chi_{1872}(467, \cdot)\) n/a 224 2
1872.2.ba \(\chi_{1872}(469, \cdot)\) n/a 240 2
1872.2.be \(\chi_{1872}(343, \cdot)\) None 0 2
1872.2.bf \(\chi_{1872}(1279, \cdot)\) 1872.2.bf.a 2 2
1872.2.bf.b 2
1872.2.bf.c 2
1872.2.bf.d 2
1872.2.bf.e 2
1872.2.bf.f 4
1872.2.bf.g 4
1872.2.bf.h 4
1872.2.bf.i 4
1872.2.bf.j 4
1872.2.bf.k 4
1872.2.bf.l 8
1872.2.bf.m 8
1872.2.bf.n 8
1872.2.bf.o 12
1872.2.bi \(\chi_{1872}(161, \cdot)\) 1872.2.bi.a 4 2
1872.2.bi.b 4
1872.2.bi.c 12
1872.2.bi.d 12
1872.2.bi.e 12
1872.2.bi.f 12
1872.2.bj \(\chi_{1872}(1097, \cdot)\) None 0 2
1872.2.bk \(\chi_{1872}(755, \cdot)\) n/a 192 2
1872.2.bm \(\chi_{1872}(181, \cdot)\) n/a 276 2
1872.2.bp \(\chi_{1872}(1061, \cdot)\) n/a 224 2
1872.2.bq \(\chi_{1872}(307, \cdot)\) n/a 276 2
1872.2.bt \(\chi_{1872}(647, \cdot)\) None 0 2
1872.2.bu \(\chi_{1872}(217, \cdot)\) None 0 2
1872.2.bx \(\chi_{1872}(575, \cdot)\) 1872.2.bx.a 8 2
1872.2.bx.b 8
1872.2.bx.c 20
1872.2.bx.d 20
1872.2.by \(\chi_{1872}(433, \cdot)\) 1872.2.by.a 2 2
1872.2.by.b 2
1872.2.by.c 2
1872.2.by.d 2
1872.2.by.e 2
1872.2.by.f 2
1872.2.by.g 4
1872.2.by.h 4
1872.2.by.i 4
1872.2.by.j 4
1872.2.by.k 4
1872.2.by.l 4
1872.2.by.m 8
1872.2.by.n 8
1872.2.by.o 16
1872.2.ca \(\chi_{1872}(745, \cdot)\) None 0 2
1872.2.cd \(\chi_{1872}(887, \cdot)\) None 0 2
1872.2.cf \(\chi_{1872}(95, \cdot)\) n/a 168 2
1872.2.ch \(\chi_{1872}(623, \cdot)\) n/a 168 2
1872.2.cl \(\chi_{1872}(263, \cdot)\) None 0 2
1872.2.cn \(\chi_{1872}(25, \cdot)\) None 0 2
1872.2.co \(\chi_{1872}(599, \cdot)\) None 0 2
1872.2.cq \(\chi_{1872}(121, \cdot)\) None 0 2
1872.2.cu \(\chi_{1872}(959, \cdot)\) n/a 168 2
1872.2.cw \(\chi_{1872}(191, \cdot)\) n/a 168 2
1872.2.cx \(\chi_{1872}(49, \cdot)\) n/a 164 2
1872.2.cz \(\chi_{1872}(601, \cdot)\) None 0 2
1872.2.db \(\chi_{1872}(311, \cdot)\) None 0 2
1872.2.de \(\chi_{1872}(313, \cdot)\) None 0 2
1872.2.dg \(\chi_{1872}(1031, \cdot)\) None 0 2
1872.2.dh \(\chi_{1872}(673, \cdot)\) n/a 164 2
1872.2.dj \(\chi_{1872}(911, \cdot)\) n/a 144 2
1872.2.dm \(\chi_{1872}(337, \cdot)\) n/a 164 2
1872.2.do \(\chi_{1872}(815, \cdot)\) n/a 168 2
1872.2.dq \(\chi_{1872}(23, \cdot)\) None 0 2
1872.2.dr \(\chi_{1872}(1465, \cdot)\) None 0 2
1872.2.dv \(\chi_{1872}(719, \cdot)\) 1872.2.dv.a 4 2
1872.2.dv.b 4
1872.2.dv.c 8
1872.2.dv.d 20
1872.2.dv.e 20
1872.2.dw \(\chi_{1872}(361, \cdot)\) None 0 2
1872.2.dz \(\chi_{1872}(503, \cdot)\) None 0 2
1872.2.ea \(\chi_{1872}(197, \cdot)\) n/a 448 4
1872.2.ed \(\chi_{1872}(19, \cdot)\) n/a 552 4
1872.2.ee \(\chi_{1872}(245, \cdot)\) n/a 1328 4
1872.2.eg \(\chi_{1872}(187, \cdot)\) n/a 1328 4
1872.2.ei \(\chi_{1872}(331, \cdot)\) n/a 1328 4
1872.2.el \(\chi_{1872}(461, \cdot)\) n/a 1328 4
1872.2.en \(\chi_{1872}(317, \cdot)\) n/a 1328 4
1872.2.ep \(\chi_{1872}(115, \cdot)\) n/a 1328 4
1872.2.eq \(\chi_{1872}(61, \cdot)\) n/a 1328 4
1872.2.es \(\chi_{1872}(491, \cdot)\) n/a 1328 4
1872.2.ev \(\chi_{1872}(131, \cdot)\) n/a 1152 4
1872.2.ey \(\chi_{1872}(829, \cdot)\) n/a 552 4
1872.2.ez \(\chi_{1872}(205, \cdot)\) n/a 1328 4
1872.2.fc \(\chi_{1872}(35, \cdot)\) n/a 448 4
1872.2.fd \(\chi_{1872}(347, \cdot)\) n/a 1328 4
1872.2.ff \(\chi_{1872}(493, \cdot)\) n/a 1328 4
1872.2.fg \(\chi_{1872}(31, \cdot)\) n/a 336 4
1872.2.fh \(\chi_{1872}(151, \cdot)\) None 0 4
1872.2.fm \(\chi_{1872}(89, \cdot)\) None 0 4
1872.2.fn \(\chi_{1872}(305, \cdot)\) n/a 112 4
1872.2.fo \(\chi_{1872}(353, \cdot)\) n/a 328 4
1872.2.fp \(\chi_{1872}(617, \cdot)\) None 0 4
1872.2.fu \(\chi_{1872}(41, \cdot)\) None 0 4
1872.2.fv \(\chi_{1872}(401, \cdot)\) n/a 328 4
1872.2.fy \(\chi_{1872}(271, \cdot)\) n/a 140 4
1872.2.fz \(\chi_{1872}(487, \cdot)\) None 0 4
1872.2.ga \(\chi_{1872}(583, \cdot)\) None 0 4
1872.2.gb \(\chi_{1872}(175, \cdot)\) n/a 336 4
1872.2.gg \(\chi_{1872}(799, \cdot)\) n/a 336 4
1872.2.gh \(\chi_{1872}(7, \cdot)\) None 0 4
1872.2.gi \(\chi_{1872}(281, \cdot)\) None 0 4
1872.2.gj \(\chi_{1872}(785, \cdot)\) n/a 328 4
1872.2.gn \(\chi_{1872}(155, \cdot)\) n/a 1328 4
1872.2.gq \(\chi_{1872}(685, \cdot)\) n/a 552 4
1872.2.gr \(\chi_{1872}(133, \cdot)\) n/a 1328 4
1872.2.gu \(\chi_{1872}(179, \cdot)\) n/a 448 4
1872.2.gv \(\chi_{1872}(563, \cdot)\) n/a 1328 4
1872.2.gx \(\chi_{1872}(157, \cdot)\) n/a 1152 4
1872.2.gy \(\chi_{1872}(277, \cdot)\) n/a 1328 4
1872.2.ha \(\chi_{1872}(419, \cdot)\) n/a 1328 4
1872.2.hd \(\chi_{1872}(643, \cdot)\) n/a 1328 4
1872.2.hf \(\chi_{1872}(605, \cdot)\) n/a 1328 4
1872.2.hh \(\chi_{1872}(5, \cdot)\) n/a 1328 4
1872.2.hi \(\chi_{1872}(499, \cdot)\) n/a 1328 4
1872.2.hk \(\chi_{1872}(67, \cdot)\) n/a 1328 4
1872.2.hm \(\chi_{1872}(149, \cdot)\) n/a 1328 4
1872.2.hp \(\chi_{1872}(163, \cdot)\) n/a 552 4
1872.2.hq \(\chi_{1872}(917, \cdot)\) n/a 448 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1872))\) into lower level spaces

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