Space of modular forms of level 3720 and weight 2

• Label: 3720.2
• Level: 3720
• Weight: 2
• Dimension: 141568
• Nonzero newspaces: 72
• Sturm bound: 1474560
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 3720 = 2^{3} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(1474560\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3720))\).

	Total	New	Old
Modular forms	374400	142960	231440
Cusp forms	362881	141568	221313
Eisenstein series	11519	1392	10127

Trace form

141568 * q - 8 * q^2 - 64 * q^3 - 120 * q^4 - 8 * q^5 - 156 * q^6 - 136 * q^7 + 16 * q^8 - 120 * q^9 - 156 * q^10 + 4 * q^12 - 16 * q^13 + 64 * q^14 - 54 * q^15 - 264 * q^16 - 20 * q^18 - 40 * q^19 + 64 * q^20 + 32 * q^21 - 56 * q^22 + 48 * q^23 - 44 * q^24 - 344 * q^25 + 32 * q^26 + 32 * q^27 - 120 * q^28 + 48 * q^29 - 82 * q^30 - 288 * q^31 - 48 * q^32 - 40 * q^33 - 152 * q^34 + 96 * q^35 - 164 * q^36 + 80 * q^37 - 80 * q^38 - 20 * q^39 - 308 * q^40 - 124 * q^42 - 72 * q^43 - 112 * q^44 - 24 * q^45 - 488 * q^46 - 32 * q^47 - 204 * q^48 - 312 * q^49 - 104 * q^50 - 480 * q^51 - 104 * q^52 - 152 * q^53 - 132 * q^54 - 268 * q^55 - 32 * q^56 - 300 * q^57 - 152 * q^58 - 168 * q^59 - 234 * q^60 - 456 * q^61 - 8 * q^62 - 488 * q^63 - 216 * q^64 - 148 * q^65 - 308 * q^66 - 288 * q^67 - 112 * q^68 - 180 * q^69 - 324 * q^70 - 272 * q^71 - 204 * q^72 - 200 * q^73 - 112 * q^74 - 264 * q^75 - 424 * q^76 - 120 * q^77 - 204 * q^78 - 248 * q^79 - 160 * q^80 - 264 * q^81 - 376 * q^82 - 160 * q^83 - 204 * q^84 + 128 * q^85 + 32 * q^86 - 180 * q^87 - 24 * q^88 + 80 * q^89 - 162 * q^90 - 232 * q^91 + 16 * q^92 + 32 * q^93 + 16 * q^94 - 48 * q^95 + 44 * q^96 - 192 * q^97 + 200 * q^98 - 236 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3720))\)

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
3720.2.a	\(\chi_{3720}(1, \cdot)\)	3720.2.a.a	1	1
		3720.2.a.b	1
		3720.2.a.c	1
		3720.2.a.d	1
		3720.2.a.e	1
		3720.2.a.f	1
		3720.2.a.g	1
		3720.2.a.h	1
		3720.2.a.i	2
		3720.2.a.j	2
		3720.2.a.k	2
		3720.2.a.l	3
		3720.2.a.m	3
		3720.2.a.n	3
		3720.2.a.o	3
		3720.2.a.p	3
		3720.2.a.q	4
		3720.2.a.r	4
		3720.2.a.s	4
		3720.2.a.t	4
		3720.2.a.u	5
		3720.2.a.v	5
		3720.2.a.w	5
3720.2.b	\(\chi_{3720}(2789, \cdot)\)	n/a	760	1
3720.2.c	\(\chi_{3720}(2171, \cdot)\)	n/a	480	1
3720.2.f	\(\chi_{3720}(3349, \cdot)\)	n/a	360	1
3720.2.g	\(\chi_{3720}(2851, \cdot)\)	n/a	256	1
3720.2.j	\(\chi_{3720}(991, \cdot)\)	None	0	1
3720.2.k	\(\chi_{3720}(1489, \cdot)\)	3720.2.k.a	2	1
		3720.2.k.b	2
		3720.2.k.c	2
		3720.2.k.d	2
		3720.2.k.e	16
		3720.2.k.f	18
		3720.2.k.g	24
		3720.2.k.h	26
3720.2.n	\(\chi_{3720}(311, \cdot)\)	None	0	1
3720.2.o	\(\chi_{3720}(929, \cdot)\)	n/a	192	1
3720.2.t	\(\chi_{3720}(1861, \cdot)\)	n/a	240	1
3720.2.u	\(\chi_{3720}(619, \cdot)\)	n/a	384	1
3720.2.x	\(\chi_{3720}(1301, \cdot)\)	n/a	512	1
3720.2.y	\(\chi_{3720}(3659, \cdot)\)	n/a	720	1
3720.2.bb	\(\chi_{3720}(1799, \cdot)\)	None	0	1
3720.2.bc	\(\chi_{3720}(3161, \cdot)\)	n/a	128	1
3720.2.bf	\(\chi_{3720}(2479, \cdot)\)	None	0	1
3720.2.bg	\(\chi_{3720}(3001, \cdot)\)	n/a	128	2
3720.2.bj	\(\chi_{3720}(497, \cdot)\)	n/a	360	2
3720.2.bk	\(\chi_{3720}(433, \cdot)\)	n/a	192	2
3720.2.bl	\(\chi_{3720}(743, \cdot)\)	None	0	2
3720.2.bm	\(\chi_{3720}(1303, \cdot)\)	None	0	2
3720.2.br	\(\chi_{3720}(2603, \cdot)\)	n/a	1520	2
3720.2.bs	\(\chi_{3720}(187, \cdot)\)	n/a	720	2
3720.2.bt	\(\chi_{3720}(1613, \cdot)\)	n/a	1440	2
3720.2.bu	\(\chi_{3720}(2293, \cdot)\)	n/a	768	2
3720.2.bx	\(\chi_{3720}(481, \cdot)\)	n/a	256	4
3720.2.by	\(\chi_{3720}(2599, \cdot)\)	None	0	2
3720.2.cb	\(\chi_{3720}(161, \cdot)\)	n/a	256	2
3720.2.cc	\(\chi_{3720}(1079, \cdot)\)	None	0	2
3720.2.cf	\(\chi_{3720}(2939, \cdot)\)	n/a	1520	2
3720.2.cg	\(\chi_{3720}(1421, \cdot)\)	n/a	1024	2
3720.2.cj	\(\chi_{3720}(739, \cdot)\)	n/a	768	2
3720.2.ck	\(\chi_{3720}(1141, \cdot)\)	n/a	512	2
3720.2.cp	\(\chi_{3720}(1049, \cdot)\)	n/a	384	2
3720.2.cq	\(\chi_{3720}(191, \cdot)\)	None	0	2
3720.2.ct	\(\chi_{3720}(769, \cdot)\)	n/a	192	2
3720.2.cu	\(\chi_{3720}(1111, \cdot)\)	None	0	2
3720.2.cx	\(\chi_{3720}(2971, \cdot)\)	n/a	512	2
3720.2.cy	\(\chi_{3720}(2629, \cdot)\)	n/a	768	2
3720.2.db	\(\chi_{3720}(1451, \cdot)\)	n/a	1024	2
3720.2.dc	\(\chi_{3720}(2909, \cdot)\)	n/a	1520	2
3720.2.dd	\(\chi_{3720}(1639, \cdot)\)	None	0	4
3720.2.dg	\(\chi_{3720}(401, \cdot)\)	n/a	512	4
3720.2.dh	\(\chi_{3720}(839, \cdot)\)	None	0	4
3720.2.dk	\(\chi_{3720}(419, \cdot)\)	n/a	3040	4
3720.2.dl	\(\chi_{3720}(461, \cdot)\)	n/a	2048	4
3720.2.do	\(\chi_{3720}(139, \cdot)\)	n/a	1536	4
3720.2.dp	\(\chi_{3720}(901, \cdot)\)	n/a	1024	4
3720.2.du	\(\chi_{3720}(89, \cdot)\)	n/a	768	4
3720.2.dv	\(\chi_{3720}(791, \cdot)\)	None	0	4
3720.2.dy	\(\chi_{3720}(529, \cdot)\)	n/a	384	4
3720.2.dz	\(\chi_{3720}(151, \cdot)\)	None	0	4
3720.2.ec	\(\chi_{3720}(91, \cdot)\)	n/a	1024	4
3720.2.ed	\(\chi_{3720}(109, \cdot)\)	n/a	1536	4
3720.2.eg	\(\chi_{3720}(1211, \cdot)\)	n/a	2048	4
3720.2.eh	\(\chi_{3720}(29, \cdot)\)	n/a	3040	4
3720.2.ei	\(\chi_{3720}(37, \cdot)\)	n/a	1536	4
3720.2.ej	\(\chi_{3720}(893, \cdot)\)	n/a	3040	4
3720.2.eo	\(\chi_{3720}(67, \cdot)\)	n/a	1536	4
3720.2.ep	\(\chi_{3720}(347, \cdot)\)	n/a	3040	4
3720.2.eq	\(\chi_{3720}(583, \cdot)\)	None	0	4
3720.2.er	\(\chi_{3720}(863, \cdot)\)	None	0	4
3720.2.ew	\(\chi_{3720}(553, \cdot)\)	n/a	384	4
3720.2.ex	\(\chi_{3720}(377, \cdot)\)	n/a	768	4
3720.2.ey	\(\chi_{3720}(121, \cdot)\)	n/a	512	8
3720.2.fb	\(\chi_{3720}(277, \cdot)\)	n/a	3072	8
3720.2.fc	\(\chi_{3720}(653, \cdot)\)	n/a	6080	8
3720.2.fd	\(\chi_{3720}(163, \cdot)\)	n/a	3072	8
3720.2.fe	\(\chi_{3720}(587, \cdot)\)	n/a	6080	8
3720.2.fj	\(\chi_{3720}(343, \cdot)\)	None	0	8
3720.2.fk	\(\chi_{3720}(23, \cdot)\)	None	0	8
3720.2.fl	\(\chi_{3720}(337, \cdot)\)	n/a	768	8
3720.2.fm	\(\chi_{3720}(233, \cdot)\)	n/a	1536	8
3720.2.fp	\(\chi_{3720}(269, \cdot)\)	n/a	6080	8
3720.2.fq	\(\chi_{3720}(131, \cdot)\)	n/a	4096	8
3720.2.ft	\(\chi_{3720}(949, \cdot)\)	n/a	3072	8
3720.2.fu	\(\chi_{3720}(331, \cdot)\)	n/a	2048	8
3720.2.fx	\(\chi_{3720}(631, \cdot)\)	None	0	8
3720.2.fy	\(\chi_{3720}(49, \cdot)\)	n/a	768	8
3720.2.gb	\(\chi_{3720}(71, \cdot)\)	None	0	8
3720.2.gc	\(\chi_{3720}(569, \cdot)\)	n/a	1536	8
3720.2.gh	\(\chi_{3720}(421, \cdot)\)	n/a	2048	8
3720.2.gi	\(\chi_{3720}(259, \cdot)\)	n/a	3072	8
3720.2.gl	\(\chi_{3720}(941, \cdot)\)	n/a	4096	8
3720.2.gm	\(\chi_{3720}(59, \cdot)\)	n/a	6080	8
3720.2.gp	\(\chi_{3720}(359, \cdot)\)	None	0	8
3720.2.gq	\(\chi_{3720}(641, \cdot)\)	n/a	1024	8
3720.2.gt	\(\chi_{3720}(79, \cdot)\)	None	0	8
3720.2.gu	\(\chi_{3720}(113, \cdot)\)	n/a	3072	16
3720.2.gv	\(\chi_{3720}(73, \cdot)\)	n/a	1536	16
3720.2.ha	\(\chi_{3720}(167, \cdot)\)	None	0	16
3720.2.hb	\(\chi_{3720}(7, \cdot)\)	None	0	16
3720.2.hc	\(\chi_{3720}(83, \cdot)\)	n/a	12160	16
3720.2.hd	\(\chi_{3720}(307, \cdot)\)	n/a	6144	16
3720.2.hi	\(\chi_{3720}(173, \cdot)\)	n/a	12160	16
3720.2.hj	\(\chi_{3720}(13, \cdot)\)	n/a	6144	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3720))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3720)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(744))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1860))\)\(^{\oplus 2}\)