Space of modular forms of level 4001 and weight 2

• Label: 4001.2
• Level: 4001
• Weight: 2
• Dimension: 665001
• Nonzero newspaces: 20
• Sturm bound: 2668000

Defining parameters

Level:	$N$	=	$4001$
Weight:	$k$	=	$2$
Nonzero newspaces:			$20$
Sturm bound:			$2668000$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4001))$.

	Total	New	Old
Modular forms	669000	669000	0
Cusp forms	665001	665001	0
Eisenstein series	3999	3999	0

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4001))$

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
4001.2.a	$\chi_{4001}(1, \cdot)$	4001.2.a.a	149	1
		4001.2.a.b	184
4001.2.b	$\chi_{4001}(4000, \cdot)$	n/a	332	1
4001.2.c	$\chi_{4001}(899, \cdot)$	n/a	664	2
4001.2.d	$\chi_{4001}(902, \cdot)$	n/a	1328	4
4001.2.e	$\chi_{4001}(70, \cdot)$	n/a	1328	4
4001.2.f	$\chi_{4001}(614, \cdot)$	n/a	1328	4
4001.2.g	$\chi_{4001}(1115, \cdot)$	n/a	2664	8
4001.2.h	$\chi_{4001}(152, \cdot)$	n/a	2656	8
4001.2.i	$\chi_{4001}(196, \cdot)$	n/a	6640	20
4001.2.k	$\chi_{4001}(673, \cdot)$	n/a	5312	16
4001.2.l	$\chi_{4001}(14, \cdot)$	n/a	6640	20
4001.2.m	$\chi_{4001}(121, \cdot)$	n/a	10656	32
4001.2.n	$\chi_{4001}(25, \cdot)$	n/a	13280	40
4001.2.o	$\chi_{4001}(26, \cdot)$	n/a	33200	100
4001.2.q	$\chi_{4001}(5, \cdot)$	n/a	26560	80
4001.2.r	$\chi_{4001}(16, \cdot)$	n/a	33200	100
4001.2.s	$\chi_{4001}(58, \cdot)$	n/a	53280	160
4001.2.t	$\chi_{4001}(4, \cdot)$	n/a	66400	200
4001.2.v	$\chi_{4001}(2, \cdot)$	n/a	132800	400
4001.2.w	$\chi_{4001}(9, \cdot)$	n/a	266400	800

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