Space of modular forms of level 4002 and weight 2

• Label: 4002.2
• Level: 4002
• Weight: 2
• Dimension: 110193
• Nonzero newspaces: 24
• Sturm bound: 1774080

Defining parameters

Level:	\( N \)	=	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1774080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4002))\).

	Total	New	Old
Modular forms	448448	110193	338255
Cusp forms	438593	110193	328400
Eisenstein series	9855	0	9855

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4002))\)

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
4002.2.a	\(\chi_{4002}(1, \cdot)\)	4002.2.a.a	1	1
		4002.2.a.b	1
		4002.2.a.c	1
		4002.2.a.d	1
		4002.2.a.e	1
		4002.2.a.f	1
		4002.2.a.g	1
		4002.2.a.h	1
		4002.2.a.i	1
		4002.2.a.j	1
		4002.2.a.k	1
		4002.2.a.l	1
		4002.2.a.m	1
		4002.2.a.n	1
		4002.2.a.o	1
		4002.2.a.p	1
		4002.2.a.q	1
		4002.2.a.r	1
		4002.2.a.s	2
		4002.2.a.t	2
		4002.2.a.u	2
		4002.2.a.v	2
		4002.2.a.w	2
		4002.2.a.x	2
		4002.2.a.y	3
		4002.2.a.z	3
		4002.2.a.ba	4
		4002.2.a.bb	4
		4002.2.a.bc	4
		4002.2.a.bd	4
		4002.2.a.be	5
		4002.2.a.bf	6
		4002.2.a.bg	7
		4002.2.a.bh	7
		4002.2.a.bi	8
		4002.2.a.bj	8
		4002.2.a.bk	8
4002.2.f	\(\chi_{4002}(4001, \cdot)\)	n/a	240	1
4002.2.g	\(\chi_{4002}(1103, \cdot)\)	n/a	224	1
4002.2.h	\(\chi_{4002}(2899, \cdot)\)	n/a	108	1
4002.2.k	\(\chi_{4002}(505, \cdot)\)	n/a	240	2
4002.2.l	\(\chi_{4002}(737, \cdot)\)	n/a	440	2
4002.2.m	\(\chi_{4002}(139, \cdot)\)	n/a	672	6
4002.2.n	\(\chi_{4002}(349, \cdot)\)	n/a	1120	10
4002.2.o	\(\chi_{4002}(415, \cdot)\)	n/a	648	6
4002.2.p	\(\chi_{4002}(413, \cdot)\)	n/a	1440	6
4002.2.q	\(\chi_{4002}(689, \cdot)\)	n/a	1440	6
4002.2.v	\(\chi_{4002}(289, \cdot)\)	n/a	1200	10
4002.2.w	\(\chi_{4002}(755, \cdot)\)	n/a	2240	10
4002.2.x	\(\chi_{4002}(521, \cdot)\)	n/a	2400	10
4002.2.bc	\(\chi_{4002}(47, \cdot)\)	n/a	2640	12
4002.2.bd	\(\chi_{4002}(229, \cdot)\)	n/a	1440	12
4002.2.bg	\(\chi_{4002}(41, \cdot)\)	n/a	4800	20
4002.2.bh	\(\chi_{4002}(157, \cdot)\)	n/a	2400	20
4002.2.bk	\(\chi_{4002}(25, \cdot)\)	n/a	7200	60
4002.2.bp	\(\chi_{4002}(5, \cdot)\)	n/a	14400	60
4002.2.bq	\(\chi_{4002}(53, \cdot)\)	n/a	14400	60
4002.2.br	\(\chi_{4002}(13, \cdot)\)	n/a	7200	60
4002.2.bu	\(\chi_{4002}(19, \cdot)\)	n/a	14400	120
4002.2.bv	\(\chi_{4002}(77, \cdot)\)	n/a	28800	120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2001))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4002))\)\(^{\oplus 1}\)