Space of modular forms of level 4761 and weight 2

• Label: 4761.2
• Level: 4761
• Weight: 2
• Dimension: 657690
• Nonzero newspaces: 16
• Sturm bound: 3351744

Defining parameters

Level:	\( N \)	=	\( 4761 = 3^{2} \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(3351744\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4761))\).

	Total	New	Old
Modular forms	843920	664031	179889
Cusp forms	831953	657690	174263
Eisenstein series	11967	6341	5626

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4761))\)

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
4761.2.a	\(\chi_{4761}(1, \cdot)\)	4761.2.a.a	1	1
		4761.2.a.b	1
		4761.2.a.c	1
		4761.2.a.d	1
		4761.2.a.e	1
		4761.2.a.f	1
		4761.2.a.g	1
		4761.2.a.h	2
		4761.2.a.i	2
		4761.2.a.j	2
		4761.2.a.k	2
		4761.2.a.l	2
		4761.2.a.m	2
		4761.2.a.n	2
		4761.2.a.o	2
		4761.2.a.p	2
		4761.2.a.q	2
		4761.2.a.r	2
		4761.2.a.s	2
		4761.2.a.t	2
		4761.2.a.u	2
		4761.2.a.v	2
		4761.2.a.w	2
		4761.2.a.x	2
		4761.2.a.y	2
		4761.2.a.z	2
		4761.2.a.ba	3
		4761.2.a.bb	4
		4761.2.a.bc	4
		4761.2.a.bd	4
		4761.2.a.be	4
		4761.2.a.bf	4
		4761.2.a.bg	4
		4761.2.a.bh	4
		4761.2.a.bi	4
		4761.2.a.bj	4
		4761.2.a.bk	4
		4761.2.a.bl	4
		4761.2.a.bm	5
		4761.2.a.bn	5
		4761.2.a.bo	5
		4761.2.a.bp	5
		4761.2.a.bq	5
		4761.2.a.br	5
		4761.2.a.bs	6
		4761.2.a.bt	10
		4761.2.a.bu	10
		4761.2.a.bv	12
		4761.2.a.bw	20
		4761.2.a.bx	20
4761.2.c	\(\chi_{4761}(4760, \cdot)\)	n/a	168	1
4761.2.e	\(\chi_{4761}(1588, \cdot)\)	n/a	968	2
4761.2.g	\(\chi_{4761}(1586, \cdot)\)	n/a	968	2
4761.2.i	\(\chi_{4761}(118, \cdot)\)	n/a	2000	10
4761.2.k	\(\chi_{4761}(359, \cdot)\)	n/a	1680	10
4761.2.m	\(\chi_{4761}(208, \cdot)\)	n/a	5038	22
4761.2.n	\(\chi_{4761}(466, \cdot)\)	n/a	9680	20
4761.2.p	\(\chi_{4761}(206, \cdot)\)	n/a	4048	22
4761.2.s	\(\chi_{4761}(263, \cdot)\)	n/a	9680	20
4761.2.u	\(\chi_{4761}(70, \cdot)\)	n/a	24200	44
4761.2.w	\(\chi_{4761}(68, \cdot)\)	n/a	24200	44
4761.2.y	\(\chi_{4761}(55, \cdot)\)	n/a	50380	220
4761.2.ba	\(\chi_{4761}(17, \cdot)\)	n/a	40480	220
4761.2.bc	\(\chi_{4761}(4, \cdot)\)	n/a	242000	440
4761.2.be	\(\chi_{4761}(5, \cdot)\)	n/a	242000	440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4761))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4761)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1587))\)\(^{\oplus 2}\)