Space of modular forms of level 5687 and weight 2

• Label: 5687.2
• Level: 5687
• Weight: 2
• Dimension: 1306341
• Nonzero newspaces: 16
• Sturm bound: 5343360

Defining parameters

Level:	\( N \)	=	\( 5687 = 11^{2} \cdot 47 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(5343360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5687))\).

	Total	New	Old
Modular forms	1343200	1318985	24215
Cusp forms	1328481	1306341	22140
Eisenstein series	14719	12644	2075

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5687))\)

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
5687.2.a	\(\chi_{5687}(1, \cdot)\)	5687.2.a.a	1	1
		5687.2.a.b	1
		5687.2.a.c	1
		5687.2.a.d	2
		5687.2.a.e	2
		5687.2.a.f	2
		5687.2.a.g	2
		5687.2.a.h	2
		5687.2.a.i	2
		5687.2.a.j	2
		5687.2.a.k	2
		5687.2.a.l	2
		5687.2.a.m	2
		5687.2.a.n	2
		5687.2.a.o	2
		5687.2.a.p	2
		5687.2.a.q	3
		5687.2.a.r	3
		5687.2.a.s	4
		5687.2.a.t	10
		5687.2.a.u	10
		5687.2.a.v	12
		5687.2.a.w	12
		5687.2.a.x	12
		5687.2.a.y	24
		5687.2.a.z	24
		5687.2.a.ba	24
		5687.2.a.bb	30
		5687.2.a.bc	42
		5687.2.a.bd	42
		5687.2.a.be	44
		5687.2.a.bf	44
		5687.2.a.bg	50
5687.2.b	\(\chi_{5687}(5686, \cdot)\)	n/a	424	1
5687.2.e	\(\chi_{5687}(565, \cdot)\)	n/a	1656	4
5687.2.h	\(\chi_{5687}(1080, \cdot)\)	n/a	1696	4
5687.2.i	\(\chi_{5687}(518, \cdot)\)	n/a	5060	10
5687.2.l	\(\chi_{5687}(516, \cdot)\)	n/a	5260	10
5687.2.m	\(\chi_{5687}(122, \cdot)\)	n/a	9394	22
5687.2.p	\(\chi_{5687}(120, \cdot)\)	n/a	9328	22
5687.2.q	\(\chi_{5687}(48, \cdot)\)	n/a	20240	40
5687.2.r	\(\chi_{5687}(46, \cdot)\)	n/a	21040	40
5687.2.u	\(\chi_{5687}(3, \cdot)\)	n/a	37312	88
5687.2.v	\(\chi_{5687}(40, \cdot)\)	n/a	37312	88
5687.2.y	\(\chi_{5687}(12, \cdot)\)	n/a	115720	220
5687.2.z	\(\chi_{5687}(10, \cdot)\)	n/a	115720	220
5687.2.bc	\(\chi_{5687}(4, \cdot)\)	n/a	462880	880
5687.2.bf	\(\chi_{5687}(13, \cdot)\)	n/a	462880	880

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5687))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5687)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(517))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5687))\)\(^{\oplus 1}\)