Space of modular forms of level 4719 and weight 2

• Label: 4719.2
• Level: 4719
• Weight: 2
• Dimension: 589568
• Nonzero newspaces: 48
• Sturm bound: 3252480

Defining parameters

Level:	\( N \)	=	\( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(3252480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4719))\).

	Total	New	Old
Modular forms	820800	595752	225048
Cusp forms	805441	589568	215873
Eisenstein series	15359	6184	9175

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4719))\)

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
4719.2.a	\(\chi_{4719}(1, \cdot)\)	4719.2.a.a	1	1
		4719.2.a.b	1
		4719.2.a.c	1
		4719.2.a.d	1
		4719.2.a.e	1
		4719.2.a.f	1
		4719.2.a.g	1
		4719.2.a.h	1
		4719.2.a.i	1
		4719.2.a.j	1
		4719.2.a.k	1
		4719.2.a.l	1
		4719.2.a.m	1
		4719.2.a.n	2
		4719.2.a.o	2
		4719.2.a.p	2
		4719.2.a.q	3
		4719.2.a.r	3
		4719.2.a.s	3
		4719.2.a.t	3
		4719.2.a.u	3
		4719.2.a.v	3
		4719.2.a.w	3
		4719.2.a.x	4
		4719.2.a.y	4
		4719.2.a.z	4
		4719.2.a.ba	5
		4719.2.a.bb	5
		4719.2.a.bc	5
		4719.2.a.bd	5
		4719.2.a.be	5
		4719.2.a.bf	5
		4719.2.a.bg	6
		4719.2.a.bh	6
		4719.2.a.bi	10
		4719.2.a.bj	10
		4719.2.a.bk	10
		4719.2.a.bl	10
		4719.2.a.bm	10
		4719.2.a.bn	10
		4719.2.a.bo	14
		4719.2.a.bp	14
		4719.2.a.bq	18
		4719.2.a.br	18
4719.2.b	\(\chi_{4719}(727, \cdot)\)	n/a	254	1
4719.2.e	\(\chi_{4719}(4718, \cdot)\)	n/a	488	1
4719.2.f	\(\chi_{4719}(3992, \cdot)\)	n/a	432	1
4719.2.i	\(\chi_{4719}(1816, \cdot)\)	n/a	510	2
4719.2.j	\(\chi_{4719}(122, \cdot)\)	n/a	980	2
4719.2.m	\(\chi_{4719}(967, \cdot)\)	n/a	504	2
4719.2.n	\(\chi_{4719}(1600, \cdot)\)	n/a	864	4
4719.2.p	\(\chi_{4719}(1088, \cdot)\)	n/a	976	2
4719.2.s	\(\chi_{4719}(1453, \cdot)\)	n/a	506	2
4719.2.t	\(\chi_{4719}(725, \cdot)\)	n/a	976	2
4719.2.x	\(\chi_{4719}(1613, \cdot)\)	n/a	1728	4
4719.2.y	\(\chi_{4719}(233, \cdot)\)	n/a	1952	4
4719.2.bb	\(\chi_{4719}(493, \cdot)\)	n/a	1008	4
4719.2.bc	\(\chi_{4719}(430, \cdot)\)	n/a	2640	10
4719.2.be	\(\chi_{4719}(241, \cdot)\)	n/a	1008	4
4719.2.bf	\(\chi_{4719}(1211, \cdot)\)	n/a	1964	4
4719.2.bh	\(\chi_{4719}(874, \cdot)\)	n/a	2016	8
4719.2.bj	\(\chi_{4719}(632, \cdot)\)	n/a	3904	8
4719.2.bk	\(\chi_{4719}(112, \cdot)\)	n/a	2016	8
4719.2.bo	\(\chi_{4719}(131, \cdot)\)	n/a	5280	10
4719.2.bp	\(\chi_{4719}(428, \cdot)\)	n/a	6120	10
4719.2.bs	\(\chi_{4719}(298, \cdot)\)	n/a	3080	10
4719.2.bu	\(\chi_{4719}(524, \cdot)\)	n/a	3904	8
4719.2.bv	\(\chi_{4719}(511, \cdot)\)	n/a	2016	8
4719.2.by	\(\chi_{4719}(887, \cdot)\)	n/a	3904	8
4719.2.ca	\(\chi_{4719}(100, \cdot)\)	n/a	6160	20
4719.2.cb	\(\chi_{4719}(109, \cdot)\)	n/a	6160	20
4719.2.ce	\(\chi_{4719}(320, \cdot)\)	n/a	12240	20
4719.2.cf	\(\chi_{4719}(157, \cdot)\)	n/a	10560	40
4719.2.cg	\(\chi_{4719}(457, \cdot)\)	n/a	4032	16
4719.2.cj	\(\chi_{4719}(245, \cdot)\)	n/a	7808	16
4719.2.cl	\(\chi_{4719}(296, \cdot)\)	n/a	12240	20
4719.2.cm	\(\chi_{4719}(166, \cdot)\)	n/a	6160	20
4719.2.cp	\(\chi_{4719}(230, \cdot)\)	n/a	12240	20
4719.2.cr	\(\chi_{4719}(25, \cdot)\)	n/a	12320	40
4719.2.cu	\(\chi_{4719}(116, \cdot)\)	n/a	24480	40
4719.2.cv	\(\chi_{4719}(248, \cdot)\)	n/a	21120	40
4719.2.cz	\(\chi_{4719}(89, \cdot)\)	n/a	24480	40
4719.2.da	\(\chi_{4719}(76, \cdot)\)	n/a	12320	40
4719.2.dc	\(\chi_{4719}(16, \cdot)\)	n/a	24640	80
4719.2.de	\(\chi_{4719}(73, \cdot)\)	n/a	24640	80
4719.2.df	\(\chi_{4719}(5, \cdot)\)	n/a	48960	80
4719.2.di	\(\chi_{4719}(29, \cdot)\)	n/a	48960	80
4719.2.dl	\(\chi_{4719}(4, \cdot)\)	n/a	24640	80
4719.2.dm	\(\chi_{4719}(17, \cdot)\)	n/a	48960	80
4719.2.do	\(\chi_{4719}(20, \cdot)\)	n/a	97920	160
4719.2.dr	\(\chi_{4719}(7, \cdot)\)	n/a	49280	160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4719))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4719)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1573))\)\(^{\oplus 2}\)