Properties

Label 3744.1
Level 3744
Weight 1
Dimension 96
Nonzero newspaces 11
Newform subspaces 22
Sturm bound 774144
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 22 \)
Sturm bound: \(774144\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3744))\).

Total New Old
Modular forms 6972 1086 5886
Cusp forms 828 96 732
Eisenstein series 6144 990 5154

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 84 12 0 0

Trace form

\( 96q + 4q^{5} - 2q^{9} + O(q^{10}) \) \( 96q + 4q^{5} - 2q^{9} - 2q^{13} + 16q^{22} - 10q^{25} + 6q^{27} - 4q^{33} + 14q^{35} - 2q^{37} + 8q^{41} - 6q^{43} - 4q^{45} - 12q^{49} + 6q^{51} - 16q^{55} - 4q^{57} + 10q^{65} + 20q^{73} - 12q^{75} + 4q^{77} + 2q^{81} - 16q^{85} - 6q^{89} + 2q^{91} + 2q^{93} + 6q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3744))\)

We only show spaces with odd 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
3744.1.b \(\chi_{3744}(1169, \cdot)\) None 0 1
3744.1.e \(\chi_{3744}(2575, \cdot)\) None 0 1
3744.1.f \(\chi_{3744}(3329, \cdot)\) None 0 1
3744.1.i \(\chi_{3744}(415, \cdot)\) None 0 1
3744.1.k \(\chi_{3744}(703, \cdot)\) None 0 1
3744.1.l \(\chi_{3744}(3041, \cdot)\) 3744.1.l.a 4 1
3744.1.l.b 4
3744.1.l.c 4
3744.1.o \(\chi_{3744}(2287, \cdot)\) 3744.1.o.a 1 1
3744.1.o.b 1
3744.1.o.c 4
3744.1.p \(\chi_{3744}(1457, \cdot)\) None 0 1
3744.1.v \(\chi_{3744}(1799, \cdot)\) None 0 2
3744.1.w \(\chi_{3744}(1513, \cdot)\) None 0 2
3744.1.z \(\chi_{3744}(521, \cdot)\) None 0 2
3744.1.bb \(\chi_{3744}(1351, \cdot)\) None 0 2
3744.1.bc \(\chi_{3744}(1009, \cdot)\) None 0 2
3744.1.bd \(\chi_{3744}(577, \cdot)\) 3744.1.bd.a 2 2
3744.1.bd.b 2
3744.1.bd.c 2
3744.1.bd.d 2
3744.1.bd.e 2
3744.1.bg \(\chi_{3744}(863, \cdot)\) None 0 2
3744.1.bh \(\chi_{3744}(1295, \cdot)\) None 0 2
3744.1.bl \(\chi_{3744}(233, \cdot)\) None 0 2
3744.1.bn \(\chi_{3744}(1639, \cdot)\) None 0 2
3744.1.bo \(\chi_{3744}(73, \cdot)\) None 0 2
3744.1.br \(\chi_{3744}(359, \cdot)\) None 0 2
3744.1.bs \(\chi_{3744}(127, \cdot)\) None 0 2
3744.1.bv \(\chi_{3744}(737, \cdot)\) 3744.1.bv.a 8 2
3744.1.bw \(\chi_{3744}(2863, \cdot)\) None 0 2
3744.1.bz \(\chi_{3744}(17, \cdot)\) None 0 2
3744.1.cb \(\chi_{3744}(257, \cdot)\) None 0 2
3744.1.cc \(\chi_{3744}(3103, \cdot)\) 3744.1.cc.a 4 2
3744.1.ce \(\chi_{3744}(3247, \cdot)\) None 0 2
3744.1.cg \(\chi_{3744}(209, \cdot)\) None 0 2
3744.1.ci \(\chi_{3744}(1039, \cdot)\) 3744.1.ci.a 6 2
3744.1.ci.b 6
3744.1.cj \(\chi_{3744}(113, \cdot)\) None 0 2
3744.1.ck \(\chi_{3744}(607, \cdot)\) 3744.1.ck.a 4 2
3744.1.cm \(\chi_{3744}(545, \cdot)\) None 0 2
3744.1.cp \(\chi_{3744}(1951, \cdot)\) None 0 2
3744.1.cr \(\chi_{3744}(1505, \cdot)\) None 0 2
3744.1.cs \(\chi_{3744}(1361, \cdot)\) None 0 2
3744.1.ct \(\chi_{3744}(751, \cdot)\) None 0 2
3744.1.cv \(\chi_{3744}(1231, \cdot)\) None 0 2
3744.1.cy \(\chi_{3744}(2129, \cdot)\) None 0 2
3744.1.da \(\chi_{3744}(1985, \cdot)\) None 0 2
3744.1.dc \(\chi_{3744}(1663, \cdot)\) None 0 2
3744.1.dd \(\chi_{3744}(833, \cdot)\) None 0 2
3744.1.df \(\chi_{3744}(1375, \cdot)\) None 0 2
3744.1.di \(\chi_{3744}(1265, \cdot)\) None 0 2
3744.1.dk \(\chi_{3744}(79, \cdot)\) None 0 2
3744.1.dl \(\chi_{3744}(2417, \cdot)\) None 0 2
3744.1.dn \(\chi_{3744}(367, \cdot)\) None 0 2
3744.1.dp \(\chi_{3744}(511, \cdot)\) None 0 2
3744.1.ds \(\chi_{3744}(1121, \cdot)\) None 0 2
3744.1.dt \(\chi_{3744}(1745, \cdot)\) None 0 2
3744.1.du \(\chi_{3744}(1135, \cdot)\) None 0 2
3744.1.dx \(\chi_{3744}(1889, \cdot)\) 3744.1.dx.a 8 2
3744.1.dy \(\chi_{3744}(991, \cdot)\) 3744.1.dy.a 4 2
3744.1.ea \(\chi_{3744}(827, \cdot)\) None 0 4
3744.1.ec \(\chi_{3744}(541, \cdot)\) None 0 4
3744.1.ef \(\chi_{3744}(235, \cdot)\) None 0 4
3744.1.eh \(\chi_{3744}(883, \cdot)\) 3744.1.eh.a 16 4
3744.1.ei \(\chi_{3744}(701, \cdot)\) None 0 4
3744.1.ek \(\chi_{3744}(53, \cdot)\) None 0 4
3744.1.en \(\chi_{3744}(395, \cdot)\) None 0 4
3744.1.ep \(\chi_{3744}(109, \cdot)\) None 0 4
3744.1.er \(\chi_{3744}(505, \cdot)\) None 0 4
3744.1.es \(\chi_{3744}(71, \cdot)\) None 0 4
3744.1.ev \(\chi_{3744}(409, \cdot)\) None 0 4
3744.1.ex \(\chi_{3744}(167, \cdot)\) None 0 4
3744.1.ez \(\chi_{3744}(1175, \cdot)\) None 0 4
3744.1.fa \(\chi_{3744}(889, \cdot)\) None 0 4
3744.1.fc \(\chi_{3744}(1129, \cdot)\) None 0 4
3744.1.fe \(\chi_{3744}(119, \cdot)\) None 0 4
3744.1.fh \(\chi_{3744}(1447, \cdot)\) None 0 4
3744.1.fj \(\chi_{3744}(185, \cdot)\) None 0 4
3744.1.fk \(\chi_{3744}(857, \cdot)\) None 0 4
3744.1.fm \(\chi_{3744}(55, \cdot)\) None 0 4
3744.1.fn \(\chi_{3744}(1303, \cdot)\) None 0 4
3744.1.fq \(\chi_{3744}(953, \cdot)\) None 0 4
3744.1.fr \(\chi_{3744}(329, \cdot)\) None 0 4
3744.1.fu \(\chi_{3744}(391, \cdot)\) None 0 4
3744.1.fy \(\chi_{3744}(385, \cdot)\) None 0 4
3744.1.fz \(\chi_{3744}(1201, \cdot)\) None 0 4
3744.1.ga \(\chi_{3744}(1103, \cdot)\) None 0 4
3744.1.gb \(\chi_{3744}(1631, \cdot)\) None 0 4
3744.1.gg \(\chi_{3744}(431, \cdot)\) None 0 4
3744.1.gh \(\chi_{3744}(1151, \cdot)\) None 0 4
3744.1.gi \(\chi_{3744}(383, \cdot)\) None 0 4
3744.1.gj \(\chi_{3744}(527, \cdot)\) None 0 4
3744.1.gm \(\chi_{3744}(97, \cdot)\) None 0 4
3744.1.gn \(\chi_{3744}(241, \cdot)\) None 0 4
3744.1.gs \(\chi_{3744}(865, \cdot)\) 3744.1.gs.a 4 4
3744.1.gs.b 4
3744.1.gs.c 4
3744.1.gt \(\chi_{3744}(145, \cdot)\) None 0 4
3744.1.gu \(\chi_{3744}(817, \cdot)\) None 0 4
3744.1.gv \(\chi_{3744}(1345, \cdot)\) None 0 4
3744.1.ha \(\chi_{3744}(47, \cdot)\) None 0 4
3744.1.hb \(\chi_{3744}(671, \cdot)\) None 0 4
3744.1.hc \(\chi_{3744}(1145, \cdot)\) None 0 4
3744.1.he \(\chi_{3744}(199, \cdot)\) None 0 4
3744.1.hf \(\chi_{3744}(439, \cdot)\) None 0 4
3744.1.hi \(\chi_{3744}(809, \cdot)\) None 0 4
3744.1.hj \(\chi_{3744}(1049, \cdot)\) None 0 4
3744.1.hm \(\chi_{3744}(103, \cdot)\) None 0 4
3744.1.hp \(\chi_{3744}(295, \cdot)\) None 0 4
3744.1.hr \(\chi_{3744}(1193, \cdot)\) None 0 4
3744.1.hs \(\chi_{3744}(1319, \cdot)\) None 0 4
3744.1.hu \(\chi_{3744}(265, \cdot)\) None 0 4
3744.1.hw \(\chi_{3744}(1033, \cdot)\) None 0 4
3744.1.hz \(\chi_{3744}(743, \cdot)\) None 0 4
3744.1.ib \(\chi_{3744}(551, \cdot)\) None 0 4
3744.1.id \(\chi_{3744}(457, \cdot)\) None 0 4
3744.1.ie \(\chi_{3744}(1367, \cdot)\) None 0 4
3744.1.ih \(\chi_{3744}(1081, \cdot)\) None 0 4
3744.1.ii \(\chi_{3744}(565, \cdot)\) None 0 8
3744.1.ik \(\chi_{3744}(227, \cdot)\) None 0 8
3744.1.im \(\chi_{3744}(515, \cdot)\) None 0 8
3744.1.io \(\chi_{3744}(37, \cdot)\) None 0 8
3744.1.ip \(\chi_{3744}(85, \cdot)\) None 0 8
3744.1.is \(\chi_{3744}(587, \cdot)\) None 0 8
3744.1.it \(\chi_{3744}(323, \cdot)\) None 0 8
3744.1.iw \(\chi_{3744}(229, \cdot)\) None 0 8
3744.1.iy \(\chi_{3744}(259, \cdot)\) None 0 8
3744.1.ja \(\chi_{3744}(547, \cdot)\) None 0 8
3744.1.jc \(\chi_{3744}(413, \cdot)\) None 0 8
3744.1.jf \(\chi_{3744}(653, \cdot)\) None 0 8
3744.1.jh \(\chi_{3744}(29, \cdot)\) None 0 8
3744.1.jj \(\chi_{3744}(173, \cdot)\) None 0 8
3744.1.jl \(\chi_{3744}(101, \cdot)\) None 0 8
3744.1.jm \(\chi_{3744}(269, \cdot)\) None 0 8
3744.1.jp \(\chi_{3744}(451, \cdot)\) None 0 8
3744.1.jq \(\chi_{3744}(43, \cdot)\) None 0 8
3744.1.js \(\chi_{3744}(355, \cdot)\) None 0 8
3744.1.ju \(\chi_{3744}(211, \cdot)\) None 0 8
3744.1.jw \(\chi_{3744}(139, \cdot)\) None 0 8
3744.1.jz \(\chi_{3744}(595, \cdot)\) None 0 8
3744.1.kb \(\chi_{3744}(365, \cdot)\) None 0 8
3744.1.kd \(\chi_{3744}(77, \cdot)\) None 0 8
3744.1.kf \(\chi_{3744}(83, \cdot)\) None 0 8
3744.1.ki \(\chi_{3744}(397, \cdot)\) None 0 8
3744.1.kj \(\chi_{3744}(349, \cdot)\) None 0 8
3744.1.km \(\chi_{3744}(11, \cdot)\) None 0 8
3744.1.kn \(\chi_{3744}(683, \cdot)\) None 0 8
3744.1.kp \(\chi_{3744}(421, \cdot)\) None 0 8
3744.1.kr \(\chi_{3744}(301, \cdot)\) None 0 8
3744.1.kt \(\chi_{3744}(371, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3744))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3744)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1872))\)\(^{\oplus 2}\)