Space of modular forms of level 3744 and weight 2

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

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 - 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

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(1))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 30}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 16}$$\oplus$$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}$