Space of modular forms of level 4165 and weight 2

• Label: 4165.2
• Level: 4165
• Weight: 2
• Dimension: 587342
• Nonzero newspaces: 72
• Sturm bound: 2709504

Defining parameters

Level:	\( N \)	=	\( 4165 = 5 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(2709504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4165))\).

	Total	New	Old
Modular forms	685056	596074	88982
Cusp forms	669697	587342	82355
Eisenstein series	15359	8732	6627

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4165))\)

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
4165.2.a	\(\chi_{4165}(1, \cdot)\)	4165.2.a.a	1	1
		4165.2.a.b	1
		4165.2.a.c	1
		4165.2.a.d	1
		4165.2.a.e	1
		4165.2.a.f	1
		4165.2.a.g	1
		4165.2.a.h	1
		4165.2.a.i	1
		4165.2.a.j	1
		4165.2.a.k	1
		4165.2.a.l	1
		4165.2.a.m	1
		4165.2.a.n	1
		4165.2.a.o	1
		4165.2.a.p	1
		4165.2.a.q	2
		4165.2.a.r	2
		4165.2.a.s	2
		4165.2.a.t	2
		4165.2.a.u	2
		4165.2.a.v	2
		4165.2.a.w	2
		4165.2.a.x	2
		4165.2.a.y	3
		4165.2.a.z	3
		4165.2.a.ba	3
		4165.2.a.bb	3
		4165.2.a.bc	3
		4165.2.a.bd	4
		4165.2.a.be	4
		4165.2.a.bf	5
		4165.2.a.bg	6
		4165.2.a.bh	6
		4165.2.a.bi	6
		4165.2.a.bj	6
		4165.2.a.bk	7
		4165.2.a.bl	7
		4165.2.a.bm	8
		4165.2.a.bn	8
		4165.2.a.bo	9
		4165.2.a.bp	9
		4165.2.a.bq	12
		4165.2.a.br	12
		4165.2.a.bs	14
		4165.2.a.bt	14
		4165.2.a.bu	18
		4165.2.a.bv	18
4165.2.c	\(\chi_{4165}(834, \cdot)\)	n/a	328	1
4165.2.d	\(\chi_{4165}(2549, \cdot)\)	n/a	360	1
4165.2.f	\(\chi_{4165}(1716, \cdot)\)	n/a	246	1
4165.2.i	\(\chi_{4165}(851, \cdot)\)	n/a	424	2
4165.2.k	\(\chi_{4165}(2206, \cdot)\)	n/a	492	2
4165.2.l	\(\chi_{4165}(293, \cdot)\)	n/a	704	2
4165.2.o	\(\chi_{4165}(783, \cdot)\)	n/a	640	2
4165.2.p	\(\chi_{4165}(832, \cdot)\)	n/a	704	2
4165.2.r	\(\chi_{4165}(2792, \cdot)\)	n/a	704	2
4165.2.t	\(\chi_{4165}(344, \cdot)\)	n/a	720	2
4165.2.x	\(\chi_{4165}(1206, \cdot)\)	n/a	480	2
4165.2.z	\(\chi_{4165}(2039, \cdot)\)	n/a	704	2
4165.2.ba	\(\chi_{4165}(324, \cdot)\)	n/a	640	2
4165.2.bc	\(\chi_{4165}(596, \cdot)\)	n/a	1776	6
4165.2.be	\(\chi_{4165}(342, \cdot)\)	n/a	1408	4
4165.2.bg	\(\chi_{4165}(246, \cdot)\)	n/a	984	4
4165.2.bh	\(\chi_{4165}(1079, \cdot)\)	n/a	1432	4
4165.2.bk	\(\chi_{4165}(587, \cdot)\)	n/a	1408	4
4165.2.bl	\(\chi_{4165}(1194, \cdot)\)	n/a	1408	4
4165.2.bo	\(\chi_{4165}(1942, \cdot)\)	n/a	1408	4
4165.2.bp	\(\chi_{4165}(1293, \cdot)\)	n/a	1280	4
4165.2.bs	\(\chi_{4165}(1342, \cdot)\)	n/a	1408	4
4165.2.bu	\(\chi_{4165}(472, \cdot)\)	n/a	1408	4
4165.2.bw	\(\chi_{4165}(361, \cdot)\)	n/a	960	4
4165.2.bz	\(\chi_{4165}(526, \cdot)\)	n/a	2016	6
4165.2.cb	\(\chi_{4165}(169, \cdot)\)	n/a	3000	6
4165.2.cc	\(\chi_{4165}(239, \cdot)\)	n/a	2688	6
4165.2.ce	\(\chi_{4165}(148, \cdot)\)	n/a	2872	8
4165.2.cg	\(\chi_{4165}(244, \cdot)\)	n/a	2816	8
4165.2.cj	\(\chi_{4165}(146, \cdot)\)	n/a	1920	8
4165.2.ck	\(\chi_{4165}(932, \cdot)\)	n/a	2872	8
4165.2.cm	\(\chi_{4165}(86, \cdot)\)	n/a	3600	12
4165.2.co	\(\chi_{4165}(423, \cdot)\)	n/a	2816	8
4165.2.cp	\(\chi_{4165}(716, \cdot)\)	n/a	1920	8
4165.2.cs	\(\chi_{4165}(569, \cdot)\)	n/a	2816	8
4165.2.cu	\(\chi_{4165}(117, \cdot)\)	n/a	2816	8
4165.2.cw	\(\chi_{4165}(64, \cdot)\)	n/a	6000	12
4165.2.cx	\(\chi_{4165}(13, \cdot)\)	n/a	6000	12
4165.2.da	\(\chi_{4165}(118, \cdot)\)	n/a	6000	12
4165.2.db	\(\chi_{4165}(188, \cdot)\)	n/a	5376	12
4165.2.dd	\(\chi_{4165}(132, \cdot)\)	n/a	6000	12
4165.2.df	\(\chi_{4165}(106, \cdot)\)	n/a	4032	12
4165.2.di	\(\chi_{4165}(494, \cdot)\)	n/a	5376	12
4165.2.dj	\(\chi_{4165}(254, \cdot)\)	n/a	6000	12
4165.2.dl	\(\chi_{4165}(16, \cdot)\)	n/a	4032	12
4165.2.do	\(\chi_{4165}(177, \cdot)\)	n/a	5632	16
4165.2.dq	\(\chi_{4165}(31, \cdot)\)	n/a	3840	16
4165.2.dt	\(\chi_{4165}(129, \cdot)\)	n/a	5632	16
4165.2.du	\(\chi_{4165}(422, \cdot)\)	n/a	5632	16
4165.2.dw	\(\chi_{4165}(83, \cdot)\)	n/a	12000	24
4165.2.dy	\(\chi_{4165}(134, \cdot)\)	n/a	12000	24
4165.2.eb	\(\chi_{4165}(36, \cdot)\)	n/a	8064	24
4165.2.ec	\(\chi_{4165}(202, \cdot)\)	n/a	12000	24
4165.2.ee	\(\chi_{4165}(81, \cdot)\)	n/a	8064	24
4165.2.eh	\(\chi_{4165}(38, \cdot)\)	n/a	12000	24
4165.2.ei	\(\chi_{4165}(33, \cdot)\)	n/a	12000	24
4165.2.el	\(\chi_{4165}(52, \cdot)\)	n/a	10752	24
4165.2.en	\(\chi_{4165}(157, \cdot)\)	n/a	12000	24
4165.2.ep	\(\chi_{4165}(4, \cdot)\)	n/a	12000	24
4165.2.er	\(\chi_{4165}(22, \cdot)\)	n/a	24000	48
4165.2.et	\(\chi_{4165}(139, \cdot)\)	n/a	24000	48
4165.2.eu	\(\chi_{4165}(6, \cdot)\)	n/a	16128	48
4165.2.ex	\(\chi_{4165}(57, \cdot)\)	n/a	24000	48
4165.2.ey	\(\chi_{4165}(87, \cdot)\)	n/a	24000	48
4165.2.fb	\(\chi_{4165}(9, \cdot)\)	n/a	24000	48
4165.2.fc	\(\chi_{4165}(121, \cdot)\)	n/a	16128	48
4165.2.fe	\(\chi_{4165}(138, \cdot)\)	n/a	24000	48
4165.2.fh	\(\chi_{4165}(23, \cdot)\)	n/a	48000	96
4165.2.fj	\(\chi_{4165}(61, \cdot)\)	n/a	32256	96
4165.2.fk	\(\chi_{4165}(24, \cdot)\)	n/a	48000	96
4165.2.fn	\(\chi_{4165}(88, \cdot)\)	n/a	48000	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4165))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4165)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 2}\)