Space of modular forms of level 6042 and weight 2

• Label: 6042.2
• Level: 6042
• Weight: 2
• Dimension: 251133
• Nonzero newspaces: 36
• Sturm bound: 4043520

Defining parameters

Level:	\( N \)	=	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(4043520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6042))\).

	Total	New	Old
Modular forms	1018368	251133	767235
Cusp forms	1003393	251133	752260
Eisenstein series	14975	0	14975

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6042))\)

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
6042.2.a	\(\chi_{6042}(1, \cdot)\)	6042.2.a.a	1	1
		6042.2.a.b	1
		6042.2.a.c	1
		6042.2.a.d	1
		6042.2.a.e	1
		6042.2.a.f	1
		6042.2.a.g	1
		6042.2.a.h	1
		6042.2.a.i	1
		6042.2.a.j	1
		6042.2.a.k	1
		6042.2.a.l	1
		6042.2.a.m	1
		6042.2.a.n	1
		6042.2.a.o	2
		6042.2.a.p	2
		6042.2.a.q	3
		6042.2.a.r	3
		6042.2.a.s	3
		6042.2.a.t	4
		6042.2.a.u	5
		6042.2.a.v	6
		6042.2.a.w	6
		6042.2.a.x	6
		6042.2.a.y	7
		6042.2.a.z	9
		6042.2.a.ba	9
		6042.2.a.bb	9
		6042.2.a.bc	9
		6042.2.a.bd	11
		6042.2.a.be	12
		6042.2.a.bf	12
		6042.2.a.bg	12
		6042.2.a.bh	13
6042.2.b	\(\chi_{6042}(4559, \cdot)\)	n/a	344	1
6042.2.e	\(\chi_{6042}(1483, \cdot)\)	n/a	160	1
6042.2.f	\(\chi_{6042}(6041, \cdot)\)	n/a	360	1
6042.2.i	\(\chi_{6042}(4453, \cdot)\)	n/a	352	2
6042.2.j	\(\chi_{6042}(2203, \cdot)\)	n/a	360	2
6042.2.m	\(\chi_{6042}(1673, \cdot)\)	n/a	648	2
6042.2.o	\(\chi_{6042}(635, \cdot)\)	n/a	720	2
6042.2.r	\(\chi_{6042}(107, \cdot)\)	n/a	688	2
6042.2.s	\(\chi_{6042}(847, \cdot)\)	n/a	360	2
6042.2.u	\(\chi_{6042}(955, \cdot)\)	n/a	1032	6
6042.2.w	\(\chi_{6042}(2839, \cdot)\)	n/a	720	4
6042.2.x	\(\chi_{6042}(83, \cdot)\)	n/a	1440	4
6042.2.z	\(\chi_{6042}(685, \cdot)\)	n/a	1968	12
6042.2.bc	\(\chi_{6042}(529, \cdot)\)	n/a	1080	6
6042.2.bd	\(\chi_{6042}(317, \cdot)\)	n/a	2160	6
6042.2.bf	\(\chi_{6042}(743, \cdot)\)	n/a	2088	6
6042.2.bj	\(\chi_{6042}(113, \cdot)\)	n/a	4320	12
6042.2.bk	\(\chi_{6042}(115, \cdot)\)	n/a	1920	12
6042.2.bn	\(\chi_{6042}(227, \cdot)\)	n/a	4320	12
6042.2.bo	\(\chi_{6042}(23, \cdot)\)	n/a	4320	12
6042.2.br	\(\chi_{6042}(295, \cdot)\)	n/a	2160	12
6042.2.bs	\(\chi_{6042}(49, \cdot)\)	n/a	4320	24
6042.2.bt	\(\chi_{6042}(191, \cdot)\)	n/a	7776	24
6042.2.bw	\(\chi_{6042}(151, \cdot)\)	n/a	4320	24
6042.2.by	\(\chi_{6042}(7, \cdot)\)	n/a	4320	24
6042.2.bz	\(\chi_{6042}(293, \cdot)\)	n/a	8640	24
6042.2.cc	\(\chi_{6042}(221, \cdot)\)	n/a	8640	24
6042.2.ce	\(\chi_{6042}(169, \cdot)\)	n/a	12960	72
6042.2.cg	\(\chi_{6042}(125, \cdot)\)	n/a	17280	48
6042.2.ch	\(\chi_{6042}(31, \cdot)\)	n/a	8640	48
6042.2.ck	\(\chi_{6042}(89, \cdot)\)	n/a	25920	72
6042.2.cm	\(\chi_{6042}(29, \cdot)\)	n/a	25920	72
6042.2.cn	\(\chi_{6042}(25, \cdot)\)	n/a	12960	72
6042.2.cq	\(\chi_{6042}(67, \cdot)\)	n/a	25920	144
6042.2.ct	\(\chi_{6042}(5, \cdot)\)	n/a	51840	144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6042))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(159))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(318))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1007))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3021))\)\(^{\oplus 2}\)