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Properties

Label 3744.2
Level 3744
Weight 2
Dimension 169326
Nonzero newspaces 100
Sturm bound 1548288
Trace bound 77

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Defining parameters

Level: \( N \) = \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(1548288\)
Trace bound: \(77\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3744))\).

Total New Old
Modular forms 393216 171306 221910
Cusp forms 380929 169326 211603
Eisenstein series 12287 1980 10307

Trace form

\( 169326 q - 120 q^{2} - 120 q^{3} - 120 q^{4} - 116 q^{5} - 160 q^{6} - 88 q^{7} - 120 q^{8} - 240 q^{9} + O(q^{10}) \) \( 169326 q - 120 q^{2} - 120 q^{3} - 120 q^{4} - 116 q^{5} - 160 q^{6} - 88 q^{7} - 120 q^{8} - 240 q^{9} - 376 q^{10} - 96 q^{11} - 160 q^{12} - 138 q^{13} - 296 q^{14} - 132 q^{15} - 160 q^{16} - 100 q^{17} - 160 q^{18} - 300 q^{19} - 152 q^{20} - 192 q^{21} - 144 q^{22} - 144 q^{23} - 160 q^{24} - 246 q^{25} - 112 q^{26} - 288 q^{27} - 320 q^{28} - 164 q^{29} - 128 q^{30} - 160 q^{31} - 80 q^{32} - 392 q^{33} - 96 q^{34} - 132 q^{35} - 112 q^{36} - 292 q^{37} + 88 q^{38} - 126 q^{39} - 32 q^{40} - 76 q^{41} - 40 q^{43} + 152 q^{44} - 64 q^{45} - 168 q^{46} + 24 q^{47} + 48 q^{48} + 78 q^{49} + 216 q^{50} - 56 q^{51} - 12 q^{52} - 132 q^{53} + 16 q^{54} - 180 q^{55} + 176 q^{56} - 144 q^{57} + 144 q^{58} + 40 q^{59} - 48 q^{60} - 132 q^{61} - 48 q^{62} - 12 q^{63} - 288 q^{64} - 248 q^{65} - 352 q^{66} - 40 q^{67} - 32 q^{68} - 32 q^{69} - 96 q^{70} + 28 q^{71} - 160 q^{72} - 628 q^{73} - 152 q^{74} + 104 q^{75} - 120 q^{76} - 88 q^{77} - 200 q^{78} - 76 q^{79} - 368 q^{80} + 80 q^{81} - 680 q^{82} + 264 q^{83} - 384 q^{84} - 208 q^{85} - 496 q^{86} + 196 q^{87} - 448 q^{88} - 156 q^{89} - 448 q^{90} - 228 q^{91} - 800 q^{92} - 160 q^{93} - 464 q^{94} + 268 q^{95} - 432 q^{96} - 308 q^{97} - 560 q^{98} + 164 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3744))\)

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
3744.2.a \(\chi_{3744}(1, \cdot)\) 3744.2.a.a 1 1
3744.2.a.b 1
3744.2.a.c 1
3744.2.a.d 1
3744.2.a.e 1
3744.2.a.f 1
3744.2.a.g 1
3744.2.a.h 1
3744.2.a.i 1
3744.2.a.j 1
3744.2.a.k 1
3744.2.a.l 1
3744.2.a.m 1
3744.2.a.n 1
3744.2.a.o 1
3744.2.a.p 1
3744.2.a.q 2
3744.2.a.r 2
3744.2.a.s 2
3744.2.a.t 2
3744.2.a.u 2
3744.2.a.v 2
3744.2.a.w 2
3744.2.a.x 2
3744.2.a.y 2
3744.2.a.z 3
3744.2.a.ba 3
3744.2.a.bb 4
3744.2.a.bc 4
3744.2.a.bd 4
3744.2.a.be 4
3744.2.a.bf 4
3744.2.c \(\chi_{3744}(3457, \cdot)\) 3744.2.c.a 2 1
3744.2.c.b 2
3744.2.c.c 2
3744.2.c.d 2
3744.2.c.e 2
3744.2.c.f 4
3744.2.c.g 4
3744.2.c.h 4
3744.2.c.i 4
3744.2.c.j 4
3744.2.c.k 4
3744.2.c.l 6
3744.2.c.m 6
3744.2.c.n 8
3744.2.c.o 8
3744.2.c.p 8
3744.2.d \(\chi_{3744}(287, \cdot)\) 3744.2.d.a 4 1
3744.2.d.b 4
3744.2.d.c 8
3744.2.d.d 8
3744.2.d.e 12
3744.2.d.f 12
3744.2.g \(\chi_{3744}(1873, \cdot)\) 3744.2.g.a 2 1
3744.2.g.b 4
3744.2.g.c 6
3744.2.g.d 8
3744.2.g.e 16
3744.2.g.f 24
3744.2.h \(\chi_{3744}(1871, \cdot)\) 3744.2.h.a 56 1
3744.2.j \(\chi_{3744}(2159, \cdot)\) 3744.2.j.a 48 1
3744.2.m \(\chi_{3744}(1585, \cdot)\) 3744.2.m.a 2 1
3744.2.m.b 2
3744.2.m.c 2
3744.2.m.d 2
3744.2.m.e 4
3744.2.m.f 8
3744.2.m.g 8
3744.2.m.h 16
3744.2.m.i 24
3744.2.n \(\chi_{3744}(3743, \cdot)\) 3744.2.n.a 28 1
3744.2.n.b 28
3744.2.q \(\chi_{3744}(1249, \cdot)\) n/a 288 2
3744.2.r \(\chi_{3744}(1537, \cdot)\) n/a 336 2
3744.2.s \(\chi_{3744}(2401, \cdot)\) n/a 336 2
3744.2.t \(\chi_{3744}(289, \cdot)\) n/a 140 2
3744.2.u \(\chi_{3744}(343, \cdot)\) None 0 2
3744.2.x \(\chi_{3744}(2969, \cdot)\) None 0 2
3744.2.y \(\chi_{3744}(935, \cdot)\) None 0 2
3744.2.ba \(\chi_{3744}(937, \cdot)\) None 0 2
3744.2.be \(\chi_{3744}(1711, \cdot)\) n/a 136 2
3744.2.bf \(\chi_{3744}(1279, \cdot)\) n/a 140 2
3744.2.bi \(\chi_{3744}(161, \cdot)\) n/a 112 2
3744.2.bj \(\chi_{3744}(593, \cdot)\) n/a 112 2
3744.2.bk \(\chi_{3744}(1223, \cdot)\) None 0 2
3744.2.bm \(\chi_{3744}(649, \cdot)\) None 0 2
3744.2.bp \(\chi_{3744}(1097, \cdot)\) None 0 2
3744.2.bq \(\chi_{3744}(2215, \cdot)\) None 0 2
3744.2.bt \(\chi_{3744}(719, \cdot)\) n/a 112 2
3744.2.bu \(\chi_{3744}(2161, \cdot)\) n/a 136 2
3744.2.bx \(\chi_{3744}(575, \cdot)\) n/a 112 2
3744.2.by \(\chi_{3744}(2305, \cdot)\) n/a 140 2
3744.2.ca \(\chi_{3744}(49, \cdot)\) n/a 328 2
3744.2.cd \(\chi_{3744}(2063, \cdot)\) n/a 328 2
3744.2.cf \(\chi_{3744}(95, \cdot)\) n/a 336 2
3744.2.ch \(\chi_{3744}(1247, \cdot)\) n/a 336 2
3744.2.cl \(\chi_{3744}(815, \cdot)\) n/a 328 2
3744.2.cn \(\chi_{3744}(337, \cdot)\) n/a 328 2
3744.2.co \(\chi_{3744}(911, \cdot)\) n/a 288 2
3744.2.cq \(\chi_{3744}(2545, \cdot)\) n/a 328 2
3744.2.cu \(\chi_{3744}(959, \cdot)\) n/a 336 2
3744.2.cw \(\chi_{3744}(191, \cdot)\) n/a 336 2
3744.2.cx \(\chi_{3744}(1921, \cdot)\) n/a 336 2
3744.2.cz \(\chi_{3744}(1777, \cdot)\) n/a 328 2
3744.2.db \(\chi_{3744}(623, \cdot)\) n/a 328 2
3744.2.de \(\chi_{3744}(625, \cdot)\) n/a 288 2
3744.2.dg \(\chi_{3744}(335, \cdot)\) n/a 328 2
3744.2.dh \(\chi_{3744}(673, \cdot)\) n/a 336 2
3744.2.dj \(\chi_{3744}(1535, \cdot)\) n/a 288 2
3744.2.dm \(\chi_{3744}(961, \cdot)\) n/a 336 2
3744.2.do \(\chi_{3744}(2687, \cdot)\) n/a 336 2
3744.2.dq \(\chi_{3744}(2831, \cdot)\) n/a 328 2
3744.2.dr \(\chi_{3744}(529, \cdot)\) n/a 328 2
3744.2.dv \(\chi_{3744}(2591, \cdot)\) n/a 112 2
3744.2.dw \(\chi_{3744}(433, \cdot)\) n/a 136 2
3744.2.dz \(\chi_{3744}(2447, \cdot)\) n/a 112 2
3744.2.eb \(\chi_{3744}(125, \cdot)\) n/a 896 4
3744.2.ed \(\chi_{3744}(1243, \cdot)\) n/a 1112 4
3744.2.ee \(\chi_{3744}(181, \cdot)\) n/a 1112 4
3744.2.eg \(\chi_{3744}(469, \cdot)\) n/a 960 4
3744.2.ej \(\chi_{3744}(755, \cdot)\) n/a 768 4
3744.2.el \(\chi_{3744}(467, \cdot)\) n/a 896 4
3744.2.em \(\chi_{3744}(1061, \cdot)\) n/a 896 4
3744.2.eo \(\chi_{3744}(307, \cdot)\) n/a 1112 4
3744.2.eq \(\chi_{3744}(665, \cdot)\) None 0 4
3744.2.et \(\chi_{3744}(1783, \cdot)\) None 0 4
3744.2.eu \(\chi_{3744}(617, \cdot)\) None 0 4
3744.2.ew \(\chi_{3744}(151, \cdot)\) None 0 4
3744.2.ey \(\chi_{3744}(1735, \cdot)\) None 0 4
3744.2.fb \(\chi_{3744}(41, \cdot)\) None 0 4
3744.2.fd \(\chi_{3744}(281, \cdot)\) None 0 4
3744.2.ff \(\chi_{3744}(1159, \cdot)\) None 0 4
3744.2.fg \(\chi_{3744}(1465, \cdot)\) None 0 4
3744.2.fi \(\chi_{3744}(23, \cdot)\) None 0 4
3744.2.fl \(\chi_{3744}(599, \cdot)\) None 0 4
3744.2.fo \(\chi_{3744}(361, \cdot)\) None 0 4
3744.2.fp \(\chi_{3744}(121, \cdot)\) None 0 4
3744.2.fs \(\chi_{3744}(503, \cdot)\) None 0 4
3744.2.ft \(\chi_{3744}(263, \cdot)\) None 0 4
3744.2.fv \(\chi_{3744}(25, \cdot)\) None 0 4
3744.2.fw \(\chi_{3744}(31, \cdot)\) n/a 672 4
3744.2.fx \(\chi_{3744}(463, \cdot)\) n/a 656 4
3744.2.gc \(\chi_{3744}(305, \cdot)\) n/a 224 4
3744.2.gd \(\chi_{3744}(449, \cdot)\) n/a 224 4
3744.2.ge \(\chi_{3744}(353, \cdot)\) n/a 672 4
3744.2.gf \(\chi_{3744}(1553, \cdot)\) n/a 656 4
3744.2.gk \(\chi_{3744}(401, \cdot)\) n/a 656 4
3744.2.gl \(\chi_{3744}(929, \cdot)\) n/a 672 4
3744.2.go \(\chi_{3744}(1567, \cdot)\) n/a 280 4
3744.2.gp \(\chi_{3744}(271, \cdot)\) n/a 272 4
3744.2.gq \(\chi_{3744}(175, \cdot)\) n/a 656 4
3744.2.gr \(\chi_{3744}(223, \cdot)\) n/a 672 4
3744.2.gw \(\chi_{3744}(799, \cdot)\) n/a 672 4
3744.2.gx \(\chi_{3744}(943, \cdot)\) n/a 656 4
3744.2.gy \(\chi_{3744}(785, \cdot)\) n/a 656 4
3744.2.gz \(\chi_{3744}(1217, \cdot)\) n/a 672 4
3744.2.hd \(\chi_{3744}(311, \cdot)\) None 0 4
3744.2.hg \(\chi_{3744}(217, \cdot)\) None 0 4
3744.2.hh \(\chi_{3744}(601, \cdot)\) None 0 4
3744.2.hk \(\chi_{3744}(647, \cdot)\) None 0 4
3744.2.hl \(\chi_{3744}(1031, \cdot)\) None 0 4
3744.2.hn \(\chi_{3744}(313, \cdot)\) None 0 4
3744.2.ho \(\chi_{3744}(745, \cdot)\) None 0 4
3744.2.hq \(\chi_{3744}(887, \cdot)\) None 0 4
3744.2.ht \(\chi_{3744}(583, \cdot)\) None 0 4
3744.2.hv \(\chi_{3744}(137, \cdot)\) None 0 4
3744.2.hx \(\chi_{3744}(473, \cdot)\) None 0 4
3744.2.hy \(\chi_{3744}(1591, \cdot)\) None 0 4
3744.2.ia \(\chi_{3744}(7, \cdot)\) None 0 4
3744.2.ic \(\chi_{3744}(713, \cdot)\) None 0 4
3744.2.if \(\chi_{3744}(487, \cdot)\) None 0 4
3744.2.ig \(\chi_{3744}(89, \cdot)\) None 0 4
3744.2.ij \(\chi_{3744}(67, \cdot)\) n/a 5344 8
3744.2.il \(\chi_{3744}(605, \cdot)\) n/a 5344 8
3744.2.in \(\chi_{3744}(317, \cdot)\) n/a 5344 8
3744.2.iq \(\chi_{3744}(115, \cdot)\) n/a 5344 8
3744.2.ir \(\chi_{3744}(163, \cdot)\) n/a 2224 8
3744.2.iu \(\chi_{3744}(917, \cdot)\) n/a 1792 8
3744.2.iv \(\chi_{3744}(245, \cdot)\) n/a 5344 8
3744.2.ix \(\chi_{3744}(187, \cdot)\) n/a 5344 8
3744.2.iz \(\chi_{3744}(157, \cdot)\) n/a 4608 8
3744.2.jb \(\chi_{3744}(493, \cdot)\) n/a 5344 8
3744.2.jd \(\chi_{3744}(35, \cdot)\) n/a 1792 8
3744.2.je \(\chi_{3744}(491, \cdot)\) n/a 5344 8
3744.2.jg \(\chi_{3744}(563, \cdot)\) n/a 5344 8
3744.2.ji \(\chi_{3744}(419, \cdot)\) n/a 5344 8
3744.2.jk \(\chi_{3744}(347, \cdot)\) n/a 5344 8
3744.2.jn \(\chi_{3744}(179, \cdot)\) n/a 1792 8
3744.2.jo \(\chi_{3744}(829, \cdot)\) n/a 2224 8
3744.2.jr \(\chi_{3744}(61, \cdot)\) n/a 5344 8
3744.2.jt \(\chi_{3744}(133, \cdot)\) n/a 5344 8
3744.2.jv \(\chi_{3744}(277, \cdot)\) n/a 5344 8
3744.2.jx \(\chi_{3744}(205, \cdot)\) n/a 5344 8
3744.2.jy \(\chi_{3744}(685, \cdot)\) n/a 2224 8
3744.2.ka \(\chi_{3744}(155, \cdot)\) n/a 5344 8
3744.2.kc \(\chi_{3744}(131, \cdot)\) n/a 4608 8
3744.2.ke \(\chi_{3744}(5, \cdot)\) n/a 5344 8
3744.2.kg \(\chi_{3744}(643, \cdot)\) n/a 5344 8
3744.2.kh \(\chi_{3744}(19, \cdot)\) n/a 2224 8
3744.2.kk \(\chi_{3744}(197, \cdot)\) n/a 1792 8
3744.2.kl \(\chi_{3744}(149, \cdot)\) n/a 5344 8
3744.2.ko \(\chi_{3744}(499, \cdot)\) n/a 5344 8
3744.2.kq \(\chi_{3744}(331, \cdot)\) n/a 5344 8
3744.2.ks \(\chi_{3744}(461, \cdot)\) n/a 5344 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3744))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1872))\)\(^{\oplus 2}\)