Space of modular forms of level 20181 and weight 2

• Label: 20181.2
• Level: 20181
• Weight: 2
• Dimension: 10574164
• Nonzero newspaces: 80
• Sturm bound: 59043840

Defining parameters

Level:	\( N \)	=	\( 20181 = 3 \cdot 7 \cdot 31^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 80 \)
Sturm bound:			\(59043840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(20181))\).

	Total	New	Old
Modular forms	14794080	10600576	4193504
Cusp forms	14727841	10574164	4153677
Eisenstein series	66239	26412	39827

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(20181))\)

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
20181.2.a	\(\chi_{20181}(1, \cdot)\)	20181.2.a.a	1	1
		20181.2.a.b	1
		20181.2.a.c	1
		20181.2.a.d	1
		20181.2.a.e	1
		20181.2.a.f	1
		20181.2.a.g	1
		20181.2.a.h	1
		20181.2.a.i	1
		20181.2.a.j	1
		20181.2.a.k	1
		20181.2.a.l	1
		20181.2.a.m	1
		20181.2.a.n	1
		20181.2.a.o	1
		20181.2.a.p	1
		20181.2.a.q	2
		20181.2.a.r	2
		20181.2.a.s	2
		20181.2.a.t	2
		20181.2.a.u	2
		20181.2.a.v	2
		20181.2.a.w	2
		20181.2.a.x	2
		20181.2.a.y	2
		20181.2.a.z	2
		20181.2.a.ba	2
		20181.2.a.bb	2
		20181.2.a.bc	2
		20181.2.a.bd	2
		20181.2.a.be	2
		20181.2.a.bf	2
		20181.2.a.bg	2
		20181.2.a.bh	2
		20181.2.a.bi	2
		20181.2.a.bj	2
		20181.2.a.bk	3
		20181.2.a.bl	3
		20181.2.a.bm	3
		20181.2.a.bn	3
		20181.2.a.bo	5
		20181.2.a.bp	5
		20181.2.a.bq	6
		20181.2.a.br	6
		20181.2.a.bs	6
		20181.2.a.bt	6
		20181.2.a.bu	7
		20181.2.a.bv	7
		20181.2.a.bw	8
		20181.2.a.bx	8
		20181.2.a.by	9
		20181.2.a.bz	9
		20181.2.a.ca	9
		20181.2.a.cb	9
		20181.2.a.cc	12
		20181.2.a.cd	12
		20181.2.a.ce	14
		20181.2.a.cf	14
		20181.2.a.cg	16
		20181.2.a.ch	16
		20181.2.a.ci	16
		20181.2.a.cj	16
		20181.2.a.ck	18
		20181.2.a.cl	18
20181.2.a.cm	28
20181.2.a.cn	28
20181.2.a.co	28
20181.2.a.cp	28
20181.2.a.cq	28
20181.2.a.cr	28
20181.2.a.cs	36
20181.2.a.ct	36
20181.2.a.cu	36
20181.2.a.cv	36
20181.2.a.cw	36
20181.2.a.cx	36
20181.2.a.cy	48
20181.2.a.cz	48
20181.2.a.da	64
20181.2.a.db	64
20181.2.c	\(\chi_{20181}(14414, \cdot)\)	n/a	1856	1
20181.2.d	\(\chi_{20181}(12494, \cdot)\)	n/a	2420	1
20181.2.f	\(\chi_{20181}(13453, \cdot)\)	n/a	1236	1
20181.2.i	\(\chi_{20181}(11533, \cdot)\)	n/a	2478	2
20181.2.j	\(\chi_{20181}(3322, \cdot)\)	n/a	2474	2
20181.2.k	\(\chi_{20181}(9088, \cdot)\)	n/a	2474	2
20181.2.l	\(\chi_{20181}(11971, \cdot)\)	n/a	1856	2
20181.2.m	\(\chi_{20181}(1492, \cdot)\)	n/a	3712	4
20181.2.o	\(\chi_{20181}(4283, \cdot)\)	n/a	4836	2
20181.2.p	\(\chi_{20181}(2444, \cdot)\)	n/a	3712	2
20181.2.s	\(\chi_{20181}(2362, \cdot)\)	n/a	2474	2
20181.2.v	\(\chi_{20181}(10132, \cdot)\)	n/a	2474	2
20181.2.y	\(\chi_{20181}(1921, \cdot)\)	n/a	2476	2
20181.2.ba	\(\chi_{20181}(6206, \cdot)\)	n/a	4838	2
20181.2.bc	\(\chi_{20181}(12932, \cdot)\)	n/a	4838	2
20181.2.bf	\(\chi_{20181}(962, \cdot)\)	n/a	4838	2
20181.2.bg	\(\chi_{20181}(5765, \cdot)\)	n/a	4836	2
20181.2.bj	\(\chi_{20181}(11972, \cdot)\)	n/a	4838	2
20181.2.bl	\(\chi_{20181}(521, \cdot)\)	n/a	4838	2
20181.2.bo	\(\chi_{20181}(1483, \cdot)\)	n/a	2476	2
20181.2.bq	\(\chi_{20181}(1294, \cdot)\)	n/a	4944	4
20181.2.bs	\(\chi_{20181}(2255, \cdot)\)	n/a	7424	4
20181.2.bv	\(\chi_{20181}(4472, \cdot)\)	n/a	9680	4
20181.2.bw	\(\chi_{20181}(547, \cdot)\)	n/a	7424	8
20181.2.bx	\(\chi_{20181}(235, \cdot)\)	n/a	9896	8
20181.2.by	\(\chi_{20181}(3271, \cdot)\)	n/a	9904	8
20181.2.bz	\(\chi_{20181}(844, \cdot)\)	n/a	9896	8
20181.2.cb	\(\chi_{20181}(3961, \cdot)\)	n/a	9904	8
20181.2.ce	\(\chi_{20181}(2648, \cdot)\)	n/a	19352	8
20181.2.cf	\(\chi_{20181}(374, \cdot)\)	n/a	19344	8
20181.2.ci	\(\chi_{20181}(1508, \cdot)\)	n/a	19352	8
20181.2.cj	\(\chi_{20181}(2039, \cdot)\)	n/a	19352	8
20181.2.cm	\(\chi_{20181}(4274, \cdot)\)	n/a	19344	8
20181.2.cn	\(\chi_{20181}(4079, \cdot)\)	n/a	19352	8
20181.2.cp	\(\chi_{20181}(145, \cdot)\)	n/a	9896	8
20181.2.ct	\(\chi_{20181}(430, \cdot)\)	n/a	9904	8
20181.2.cw	\(\chi_{20181}(115, \cdot)\)	n/a	9896	8
20181.2.cy	\(\chi_{20181}(1196, \cdot)\)	n/a	19344	8
20181.2.db	\(\chi_{20181}(4922, \cdot)\)	n/a	14848	8
20181.2.dc	\(\chi_{20181}(652, \cdot)\)	n/a	29760	30
20181.2.df	\(\chi_{20181}(433, \cdot)\)	n/a	39720	30
20181.2.dh	\(\chi_{20181}(125, \cdot)\)	n/a	79200	30
20181.2.di	\(\chi_{20181}(92, \cdot)\)	n/a	59520	30
20181.2.dk	\(\chi_{20181}(211, \cdot)\)	n/a	59520	60
20181.2.dl	\(\chi_{20181}(25, \cdot)\)	n/a	79380	60
20181.2.dm	\(\chi_{20181}(67, \cdot)\)	n/a	79380	60
20181.2.dn	\(\chi_{20181}(373, \cdot)\)	n/a	79320	60
20181.2.do	\(\chi_{20181}(64, \cdot)\)	n/a	119040	120
20181.2.dp	\(\chi_{20181}(181, \cdot)\)	n/a	79320	60
20181.2.ds	\(\chi_{20181}(5, \cdot)\)	n/a	158460	60
20181.2.du	\(\chi_{20181}(254, \cdot)\)	n/a	158460	60
20181.2.dx	\(\chi_{20181}(464, \cdot)\)	n/a	158520	60
20181.2.dy	\(\chi_{20181}(311, \cdot)\)	n/a	158520	60
20181.2.eb	\(\chi_{20181}(563, \cdot)\)	n/a	158460	60
20181.2.ed	\(\chi_{20181}(212, \cdot)\)	n/a	158460	60
20181.2.ef	\(\chi_{20181}(61, \cdot)\)	n/a	79320	60
20181.2.ei	\(\chi_{20181}(367, \cdot)\)	n/a	79380	60
20181.2.el	\(\chi_{20181}(409, \cdot)\)	n/a	79380	60
20181.2.eo	\(\chi_{20181}(491, \cdot)\)	n/a	119040	60
20181.2.ep	\(\chi_{20181}(335, \cdot)\)	n/a	158520	60
20181.2.er	\(\chi_{20181}(188, \cdot)\)	n/a	316800	120
20181.2.eu	\(\chi_{20181}(29, \cdot)\)	n/a	238080	120
20181.2.ew	\(\chi_{20181}(139, \cdot)\)	n/a	158880	120
20181.2.ey	\(\chi_{20181}(142, \cdot)\)	n/a	317520	240
20181.2.ez	\(\chi_{20181}(4, \cdot)\)	n/a	317280	240
20181.2.fa	\(\chi_{20181}(100, \cdot)\)	n/a	317520	240
20181.2.fb	\(\chi_{20181}(169, \cdot)\)	n/a	238080	240
20181.2.fc	\(\chi_{20181}(176, \cdot)\)	n/a	476160	240
20181.2.ff	\(\chi_{20181}(20, \cdot)\)	n/a	634080	240
20181.2.fh	\(\chi_{20181}(52, \cdot)\)	n/a	317520	240
20181.2.fk	\(\chi_{20181}(178, \cdot)\)	n/a	317280	240
20181.2.fo	\(\chi_{20181}(136, \cdot)\)	n/a	317520	240
20181.2.fq	\(\chi_{20181}(38, \cdot)\)	n/a	633840	240
20181.2.fr	\(\chi_{20181}(23, \cdot)\)	n/a	634080	240
20181.2.fu	\(\chi_{20181}(11, \cdot)\)	n/a	633840	240
20181.2.fv	\(\chi_{20181}(80, \cdot)\)	n/a	633840	240
20181.2.fy	\(\chi_{20181}(47, \cdot)\)	n/a	634080	240
20181.2.fz	\(\chi_{20181}(44, \cdot)\)	n/a	633840	240
20181.2.gc	\(\chi_{20181}(13, \cdot)\)	n/a	317280	240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(20181))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(20181)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(217))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(651))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2883))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6727))\)\(^{\oplus 2}\)