Space of modular forms of level 4005 and weight 2

• Label: 4005.2
• Level: 4005
• Weight: 2
• Dimension: 411366
• Nonzero newspaces: 56
• Sturm bound: 2280960

Defining parameters

Level:	\( N \)	=	\( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(2280960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4005))\).

	Total	New	Old
Modular forms	575872	416066	159806
Cusp forms	564609	411366	153243
Eisenstein series	11263	4700	6563

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4005))\)

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
4005.2.a	\(\chi_{4005}(1, \cdot)\)	4005.2.a.a	1	1
		4005.2.a.b	1
		4005.2.a.c	1
		4005.2.a.d	1
		4005.2.a.e	2
		4005.2.a.f	2
		4005.2.a.g	2
		4005.2.a.h	2
		4005.2.a.i	3
		4005.2.a.j	3
		4005.2.a.k	4
		4005.2.a.l	4
		4005.2.a.m	4
		4005.2.a.n	6
		4005.2.a.o	7
		4005.2.a.p	8
		4005.2.a.q	9
		4005.2.a.r	10
		4005.2.a.s	10
		4005.2.a.t	10
		4005.2.a.u	12
		4005.2.a.v	12
		4005.2.a.w	17
		4005.2.a.x	17
4005.2.c	\(\chi_{4005}(2404, \cdot)\)	n/a	220	1
4005.2.e	\(\chi_{4005}(2224, \cdot)\)	n/a	224	1
4005.2.g	\(\chi_{4005}(3826, \cdot)\)	n/a	150	1
4005.2.i	\(\chi_{4005}(1336, \cdot)\)	n/a	704	2
4005.2.k	\(\chi_{4005}(1369, \cdot)\)	n/a	444	2
4005.2.l	\(\chi_{4005}(233, \cdot)\)	n/a	360	2
4005.2.n	\(\chi_{4005}(2402, \cdot)\)	n/a	360	2
4005.2.o	\(\chi_{4005}(2582, \cdot)\)	n/a	352	2
4005.2.r	\(\chi_{4005}(2348, \cdot)\)	n/a	360	2
4005.2.u	\(\chi_{4005}(856, \cdot)\)	n/a	300	2
4005.2.w	\(\chi_{4005}(1156, \cdot)\)	n/a	720	2
4005.2.y	\(\chi_{4005}(889, \cdot)\)	n/a	1072	2
4005.2.ba	\(\chi_{4005}(1069, \cdot)\)	n/a	1056	2
4005.2.bd	\(\chi_{4005}(611, \cdot)\)	n/a	480	4
4005.2.be	\(\chi_{4005}(838, \cdot)\)	n/a	892	4
4005.2.bf	\(\chi_{4005}(37, \cdot)\)	n/a	892	4
4005.2.bj	\(\chi_{4005}(764, \cdot)\)	n/a	720	4
4005.2.bk	\(\chi_{4005}(91, \cdot)\)	n/a	1500	10
4005.2.bl	\(\chi_{4005}(301, \cdot)\)	n/a	1440	4
4005.2.bo	\(\chi_{4005}(767, \cdot)\)	n/a	2144	4
4005.2.br	\(\chi_{4005}(713, \cdot)\)	n/a	2112	4
4005.2.bs	\(\chi_{4005}(533, \cdot)\)	n/a	2144	4
4005.2.bu	\(\chi_{4005}(212, \cdot)\)	n/a	2144	4
4005.2.bv	\(\chi_{4005}(34, \cdot)\)	n/a	2144	4
4005.2.by	\(\chi_{4005}(406, \cdot)\)	n/a	1500	10
4005.2.ca	\(\chi_{4005}(289, \cdot)\)	n/a	2240	10
4005.2.cc	\(\chi_{4005}(64, \cdot)\)	n/a	2240	10
4005.2.ce	\(\chi_{4005}(344, \cdot)\)	n/a	4288	8
4005.2.ci	\(\chi_{4005}(457, \cdot)\)	n/a	4288	8
4005.2.cj	\(\chi_{4005}(52, \cdot)\)	n/a	4288	8
4005.2.ck	\(\chi_{4005}(101, \cdot)\)	n/a	2880	8
4005.2.cm	\(\chi_{4005}(16, \cdot)\)	n/a	7200	20
4005.2.cn	\(\chi_{4005}(136, \cdot)\)	n/a	3000	20
4005.2.cq	\(\chi_{4005}(53, \cdot)\)	n/a	3600	20
4005.2.ct	\(\chi_{4005}(8, \cdot)\)	n/a	3600	20
4005.2.cu	\(\chi_{4005}(278, \cdot)\)	n/a	3600	20
4005.2.cw	\(\chi_{4005}(17, \cdot)\)	n/a	3600	20
4005.2.cx	\(\chi_{4005}(109, \cdot)\)	n/a	4440	20
4005.2.da	\(\chi_{4005}(4, \cdot)\)	n/a	10720	20
4005.2.dc	\(\chi_{4005}(139, \cdot)\)	n/a	10720	20
4005.2.de	\(\chi_{4005}(526, \cdot)\)	n/a	7200	20
4005.2.dg	\(\chi_{4005}(224, \cdot)\)	n/a	7200	40
4005.2.dk	\(\chi_{4005}(28, \cdot)\)	n/a	8920	40
4005.2.dl	\(\chi_{4005}(82, \cdot)\)	n/a	8920	40
4005.2.dm	\(\chi_{4005}(26, \cdot)\)	n/a	4800	40
4005.2.dp	\(\chi_{4005}(49, \cdot)\)	n/a	21440	40
4005.2.dq	\(\chi_{4005}(47, \cdot)\)	n/a	21440	40
4005.2.ds	\(\chi_{4005}(203, \cdot)\)	n/a	21440	40
4005.2.dt	\(\chi_{4005}(2, \cdot)\)	n/a	21440	40
4005.2.dw	\(\chi_{4005}(68, \cdot)\)	n/a	21440	40
4005.2.dz	\(\chi_{4005}(106, \cdot)\)	n/a	14400	40
4005.2.eb	\(\chi_{4005}(41, \cdot)\)	n/a	28800	80
4005.2.ec	\(\chi_{4005}(43, \cdot)\)	n/a	42880	80
4005.2.ed	\(\chi_{4005}(7, \cdot)\)	n/a	42880	80
4005.2.eh	\(\chi_{4005}(14, \cdot)\)	n/a	42880	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(267))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(801))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1335))\)\(^{\oplus 2}\)