Space of modular forms of level 4000 and weight 1

• Label: 4000.1
• Level: 4000
• Weight: 1
• Dimension: 128
• Nonzero newspaces: 9
• Newform subspaces: 16
• Sturm bound: 960000
• Trace bound: 29

Defining parameters

Level:	\( N \)	=	\( 4000 = 2^{5} \cdot 5^{3} \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(960000\)
Trace bound:			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(4000))\).

	Total	New	Old
Modular forms	6292	1408	4884
Cusp forms	532	128	404
Eisenstein series	5760	1280	4480

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	88	0	0	40

Trace form

\( 128 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(4000))\)

We only show spaces with odd 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
4000.1.b	\(\chi_{4000}(2751, \cdot)\)	4000.1.b.a	4	1
		4000.1.b.b	4
4000.1.e	\(\chi_{4000}(1999, \cdot)\)	4000.1.e.a	2	1
		4000.1.e.b	2
4000.1.g	\(\chi_{4000}(751, \cdot)\)	4000.1.g.a	4	1
4000.1.h	\(\chi_{4000}(3999, \cdot)\)	4000.1.h.a	4	1
		4000.1.h.b	4
4000.1.i	\(\chi_{4000}(57, \cdot)\)	None	0	2
4000.1.k	\(\chi_{4000}(999, \cdot)\)	None	0	2
4000.1.m	\(\chi_{4000}(2193, \cdot)\)	None	0	2
4000.1.p	\(\chi_{4000}(193, \cdot)\)	4000.1.p.a	8	2
		4000.1.p.b	8
4000.1.r	\(\chi_{4000}(1751, \cdot)\)	None	0	2
4000.1.t	\(\chi_{4000}(2057, \cdot)\)	None	0	2
4000.1.w	\(\chi_{4000}(1557, \cdot)\)	None	0	4
4000.1.x	\(\chi_{4000}(251, \cdot)\)	None	0	4
4000.1.z	\(\chi_{4000}(499, \cdot)\)	None	0	4
4000.1.bc	\(\chi_{4000}(557, \cdot)\)	None	0	4
4000.1.bd	\(\chi_{4000}(1551, \cdot)\)	None	0	4
4000.1.bf	\(\chi_{4000}(799, \cdot)\)	4000.1.bf.a	8	4
		4000.1.bf.b	8
4000.1.bh	\(\chi_{4000}(351, \cdot)\)	4000.1.bh.a	8	4
4000.1.bi	\(\chi_{4000}(399, \cdot)\)	None	0	4
4000.1.bk	\(\chi_{4000}(457, \cdot)\)	None	0	8
4000.1.bn	\(\chi_{4000}(199, \cdot)\)	None	0	8
4000.1.bo	\(\chi_{4000}(257, \cdot)\)	4000.1.bo.a	8	8
		4000.1.bo.b	8
		4000.1.bo.c	8
4000.1.br	\(\chi_{4000}(593, \cdot)\)	None	0	8
4000.1.bs	\(\chi_{4000}(151, \cdot)\)	None	0	8
4000.1.bv	\(\chi_{4000}(393, \cdot)\)	None	0	8
4000.1.bx	\(\chi_{4000}(93, \cdot)\)	None	0	16
4000.1.ca	\(\chi_{4000}(99, \cdot)\)	None	0	16
4000.1.cc	\(\chi_{4000}(51, \cdot)\)	None	0	16
4000.1.cd	\(\chi_{4000}(157, \cdot)\)	None	0	16
4000.1.cf	\(\chi_{4000}(159, \cdot)\)	None	0	20
4000.1.cg	\(\chi_{4000}(79, \cdot)\)	None	0	20
4000.1.ci	\(\chi_{4000}(111, \cdot)\)	None	0	20
4000.1.cl	\(\chi_{4000}(31, \cdot)\)	None	0	20
4000.1.cm	\(\chi_{4000}(71, \cdot)\)	None	0	40
4000.1.cp	\(\chi_{4000}(73, \cdot)\)	None	0	40
4000.1.cq	\(\chi_{4000}(33, \cdot)\)	4000.1.cq.a	40	40
4000.1.ct	\(\chi_{4000}(17, \cdot)\)	None	0	40
4000.1.cu	\(\chi_{4000}(137, \cdot)\)	None	0	40
4000.1.cx	\(\chi_{4000}(39, \cdot)\)	None	0	40
4000.1.cz	\(\chi_{4000}(53, \cdot)\)	None	0	80
4000.1.db	\(\chi_{4000}(11, \cdot)\)	None	0	80
4000.1.dc	\(\chi_{4000}(19, \cdot)\)	None	0	80
4000.1.de	\(\chi_{4000}(13, \cdot)\)	None	0	80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(4000))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(4000)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1000))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2000))\)\(^{\oplus 2}\)