Space of modular forms of level 6018 and weight 2

• Label: 6018.2
• Level: 6018
• Weight: 2
• Dimension: 248673
• Nonzero newspaces: 20
• Sturm bound: 4008960

Defining parameters

Level:	\( N \)	=	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(4008960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6018))\).

	Total	New	Old
Modular forms	1009664	248673	760991
Cusp forms	994817	248673	746144
Eisenstein series	14847	0	14847

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6018))\)

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
6018.2.a	\(\chi_{6018}(1, \cdot)\)	6018.2.a.a	1	1
		6018.2.a.b	1
		6018.2.a.c	1
		6018.2.a.d	1
		6018.2.a.e	1
		6018.2.a.f	1
		6018.2.a.g	1
		6018.2.a.h	1
		6018.2.a.i	1
		6018.2.a.j	1
		6018.2.a.k	1
		6018.2.a.l	1
		6018.2.a.m	3
		6018.2.a.n	4
		6018.2.a.o	4
		6018.2.a.p	5
		6018.2.a.q	6
		6018.2.a.r	6
		6018.2.a.s	8
		6018.2.a.t	8
		6018.2.a.u	9
		6018.2.a.v	9
		6018.2.a.w	9
		6018.2.a.x	10
		6018.2.a.y	10
		6018.2.a.z	11
		6018.2.a.ba	12
		6018.2.a.bb	13
		6018.2.a.bc	14
6018.2.b	\(\chi_{6018}(4249, \cdot)\)	n/a	176	1
6018.2.e	\(\chi_{6018}(1769, \cdot)\)	n/a	320	1
6018.2.f	\(\chi_{6018}(6017, \cdot)\)	n/a	360	1
6018.2.i	\(\chi_{6018}(353, \cdot)\)	n/a	720	2
6018.2.l	\(\chi_{6018}(4603, \cdot)\)	n/a	352	2
6018.2.n	\(\chi_{6018}(355, \cdot)\)	n/a	688	4
6018.2.o	\(\chi_{6018}(2123, \cdot)\)	n/a	1440	4
6018.2.q	\(\chi_{6018}(473, \cdot)\)	n/a	2784	8
6018.2.t	\(\chi_{6018}(235, \cdot)\)	n/a	1440	8
6018.2.u	\(\chi_{6018}(205, \cdot)\)	n/a	4480	28
6018.2.x	\(\chi_{6018}(101, \cdot)\)	n/a	10080	28
6018.2.y	\(\chi_{6018}(443, \cdot)\)	n/a	8960	28
6018.2.bb	\(\chi_{6018}(169, \cdot)\)	n/a	5040	28
6018.2.bc	\(\chi_{6018}(361, \cdot)\)	n/a	10080	56
6018.2.bf	\(\chi_{6018}(47, \cdot)\)	n/a	20160	56
6018.2.bh	\(\chi_{6018}(77, \cdot)\)	n/a	40320	112
6018.2.bi	\(\chi_{6018}(19, \cdot)\)	n/a	20160	112
6018.2.bk	\(\chi_{6018}(31, \cdot)\)	n/a	40320	224
6018.2.bn	\(\chi_{6018}(5, \cdot)\)	n/a	80640	224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2006))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3009))\)\(^{\oplus 2}\)