Space of modular forms of level 4018 and weight 2

• Label: 4018.2
• Level: 4018
• Weight: 2
• Dimension: 157800
• Nonzero newspaces: 32
• Sturm bound: 1975680

Defining parameters

Level:	\( N \)	=	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(1975680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4018))\).

	Total	New	Old
Modular forms	498720	157800	340920
Cusp forms	489121	157800	331321
Eisenstein series	9599	0	9599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4018))\)

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
4018.2.a	\(\chi_{4018}(1, \cdot)\)	4018.2.a.a	1	1
		4018.2.a.b	1
		4018.2.a.c	1
		4018.2.a.d	1
		4018.2.a.e	1
		4018.2.a.f	1
		4018.2.a.g	1
		4018.2.a.h	1
		4018.2.a.i	1
		4018.2.a.j	1
		4018.2.a.k	1
		4018.2.a.l	1
		4018.2.a.m	1
		4018.2.a.n	1
		4018.2.a.o	1
		4018.2.a.p	1
		4018.2.a.q	1
		4018.2.a.r	1
		4018.2.a.s	1
		4018.2.a.t	2
		4018.2.a.u	2
		4018.2.a.v	2
		4018.2.a.w	2
		4018.2.a.x	2
		4018.2.a.y	2
		4018.2.a.z	2
		4018.2.a.ba	2
		4018.2.a.bb	2
		4018.2.a.bc	2
		4018.2.a.bd	3
		4018.2.a.be	3
		4018.2.a.bf	3
		4018.2.a.bg	3
		4018.2.a.bh	3
		4018.2.a.bi	4
		4018.2.a.bj	4
		4018.2.a.bk	4
		4018.2.a.bl	4
		4018.2.a.bm	4
		4018.2.a.bn	6
		4018.2.a.bo	6
		4018.2.a.bp	6
		4018.2.a.bq	6
		4018.2.a.br	10
		4018.2.a.bs	10
		4018.2.a.bt	10
		4018.2.a.bu	10
4018.2.c	\(\chi_{4018}(491, \cdot)\)	n/a	144	1
4018.2.e	\(\chi_{4018}(165, \cdot)\)	n/a	264	2
4018.2.f	\(\chi_{4018}(2059, \cdot)\)	n/a	286	2
4018.2.h	\(\chi_{4018}(1863, \cdot)\)	n/a	576	4
4018.2.j	\(\chi_{4018}(655, \cdot)\)	n/a	280	2
4018.2.l	\(\chi_{4018}(575, \cdot)\)	n/a	1104	6
4018.2.n	\(\chi_{4018}(489, \cdot)\)	n/a	560	4
4018.2.o	\(\chi_{4018}(687, \cdot)\)	n/a	576	4
4018.2.s	\(\chi_{4018}(1157, \cdot)\)	n/a	560	4
4018.2.u	\(\chi_{4018}(1065, \cdot)\)	n/a	1176	6
4018.2.w	\(\chi_{4018}(961, \cdot)\)	n/a	1120	8
4018.2.y	\(\chi_{4018}(197, \cdot)\)	n/a	1144	8
4018.2.z	\(\chi_{4018}(247, \cdot)\)	n/a	2256	12
4018.2.ba	\(\chi_{4018}(325, \cdot)\)	n/a	1120	8
4018.2.bd	\(\chi_{4018}(155, \cdot)\)	n/a	2352	12
4018.2.bg	\(\chi_{4018}(373, \cdot)\)	n/a	1120	8
4018.2.bh	\(\chi_{4018}(57, \cdot)\)	n/a	4704	24
4018.2.bi	\(\chi_{4018}(97, \cdot)\)	n/a	2240	16
4018.2.bl	\(\chi_{4018}(81, \cdot)\)	n/a	2352	12
4018.2.bo	\(\chi_{4018}(27, \cdot)\)	n/a	4704	24
4018.2.bp	\(\chi_{4018}(361, \cdot)\)	n/a	2240	16
4018.2.bt	\(\chi_{4018}(113, \cdot)\)	n/a	4704	24
4018.2.bu	\(\chi_{4018}(9, \cdot)\)	n/a	4704	24
4018.2.bw	\(\chi_{4018}(37, \cdot)\)	n/a	9408	48
4018.2.by	\(\chi_{4018}(19, \cdot)\)	n/a	4480	32
4018.2.bz	\(\chi_{4018}(43, \cdot)\)	n/a	9408	48
4018.2.cb	\(\chi_{4018}(3, \cdot)\)	n/a	9408	48
4018.2.cd	\(\chi_{4018}(23, \cdot)\)	n/a	9408	48
4018.2.cg	\(\chi_{4018}(13, \cdot)\)	n/a	18816	96
4018.2.cj	\(\chi_{4018}(39, \cdot)\)	n/a	18816	96
4018.2.cl	\(\chi_{4018}(17, \cdot)\)	n/a	37632	192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2009))\)\(^{\oplus 2}\)