Space of modular forms of level 5010 and weight 2

• Label: 5010.2
• Level: 5010
• Weight: 2
• Dimension: 153369
• Nonzero newspaces: 12
• Sturm bound: 2677248

Defining parameters

Level:	\( N \)	=	\( 5010 = 2 \cdot 3 \cdot 5 \cdot 167 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(2677248\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5010))\).

	Total	New	Old
Modular forms	674624	153369	521255
Cusp forms	664001	153369	510632
Eisenstein series	10623	0	10623

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5010))\)

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
5010.2.a	\(\chi_{5010}(1, \cdot)\)	5010.2.a.a	1	1
		5010.2.a.b	1
		5010.2.a.c	1
		5010.2.a.d	1
		5010.2.a.e	1
		5010.2.a.f	1
		5010.2.a.g	1
		5010.2.a.h	1
		5010.2.a.i	2
		5010.2.a.j	2
		5010.2.a.k	2
		5010.2.a.l	2
		5010.2.a.m	3
		5010.2.a.n	3
		5010.2.a.o	3
		5010.2.a.p	3
		5010.2.a.q	4
		5010.2.a.r	4
		5010.2.a.s	4
		5010.2.a.t	5
		5010.2.a.u	5
		5010.2.a.v	5
		5010.2.a.w	5
		5010.2.a.x	6
		5010.2.a.y	7
		5010.2.a.z	7
		5010.2.a.ba	9
		5010.2.a.bb	10
		5010.2.a.bc	10
5010.2.c	\(\chi_{5010}(5009, \cdot)\)	n/a	336	1
5010.2.d	\(\chi_{5010}(4009, \cdot)\)	n/a	164	1
5010.2.f	\(\chi_{5010}(1001, \cdot)\)	n/a	224	1
5010.2.i	\(\chi_{5010}(1337, \cdot)\)	n/a	664	2
5010.2.k	\(\chi_{5010}(667, \cdot)\)	n/a	336	2
5010.2.m	\(\chi_{5010}(31, \cdot)\)	n/a	9184	82
5010.2.p	\(\chi_{5010}(41, \cdot)\)	n/a	18368	82
5010.2.r	\(\chi_{5010}(19, \cdot)\)	n/a	13776	82
5010.2.s	\(\chi_{5010}(59, \cdot)\)	n/a	27552	82
5010.2.v	\(\chi_{5010}(13, \cdot)\)	n/a	27552	164
5010.2.x	\(\chi_{5010}(47, \cdot)\)	n/a	55104	164

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(835))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1670))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2505))\)\(^{\oplus 2}\)