Space of modular forms of level 3744 and weight 1

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

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

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

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 available 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(1))$$^{\oplus 36}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 30}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 24}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 20}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 18}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 16}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 18}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 10}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(26))$$^{\oplus 15}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(48))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(78))$$^{\oplus 10}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(96))$$^{\oplus 4}$$\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(234))$$^{\oplus 5}$$\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}$