Space of modular forms of level 5635 and weight 2

• Label: 5635.2
• Level: 5635
• Weight: 2
• Dimension: 1082136
• Nonzero newspaces: 48
• Sturm bound: 4967424

Defining parameters

Level:	\( N \)	=	\( 5635 = 5 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(4967424\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5635))\).

	Total	New	Old
Modular forms	1252416	1094360	158056
Cusp forms	1231297	1082136	149161
Eisenstein series	21119	12224	8895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5635))\)

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
5635.2.a	\(\chi_{5635}(1, \cdot)\)	5635.2.a.a	1	1
		5635.2.a.b	1
		5635.2.a.c	1
		5635.2.a.d	1
		5635.2.a.e	1
		5635.2.a.f	1
		5635.2.a.g	1
		5635.2.a.h	1
		5635.2.a.i	1
		5635.2.a.j	1
		5635.2.a.k	1
		5635.2.a.l	1
		5635.2.a.m	1
		5635.2.a.n	2
		5635.2.a.o	2
		5635.2.a.p	2
		5635.2.a.q	2
		5635.2.a.r	3
		5635.2.a.s	4
		5635.2.a.t	4
		5635.2.a.u	4
		5635.2.a.v	4
		5635.2.a.w	4
		5635.2.a.x	5
		5635.2.a.y	5
		5635.2.a.z	6
		5635.2.a.ba	6
		5635.2.a.bb	8
		5635.2.a.bc	12
		5635.2.a.bd	12
		5635.2.a.be	13
		5635.2.a.bf	13
		5635.2.a.bg	13
		5635.2.a.bh	13
		5635.2.a.bi	15
		5635.2.a.bj	15
		5635.2.a.bk	16
		5635.2.a.bl	16
		5635.2.a.bm	17
		5635.2.a.bn	17
		5635.2.a.bo	28
		5635.2.a.bp	28
5635.2.c	\(\chi_{5635}(4509, \cdot)\)	n/a	450	1
5635.2.d	\(\chi_{5635}(5634, \cdot)\)	n/a	472	1
5635.2.f	\(\chi_{5635}(1126, \cdot)\)	n/a	320	1
5635.2.i	\(\chi_{5635}(116, \cdot)\)	n/a	584	2
5635.2.k	\(\chi_{5635}(783, \cdot)\)	n/a	880	2
5635.2.l	\(\chi_{5635}(2598, \cdot)\)	n/a	964	2
5635.2.p	\(\chi_{5635}(1011, \cdot)\)	n/a	640	2
5635.2.r	\(\chi_{5635}(3449, \cdot)\)	n/a	944	2
5635.2.s	\(\chi_{5635}(1059, \cdot)\)	n/a	880	2
5635.2.u	\(\chi_{5635}(806, \cdot)\)	n/a	2448	6
5635.2.v	\(\chi_{5635}(246, \cdot)\)	n/a	3280	10
5635.2.w	\(\chi_{5635}(668, \cdot)\)	n/a	1760	4
5635.2.z	\(\chi_{5635}(1402, \cdot)\)	n/a	1888	4
5635.2.bc	\(\chi_{5635}(321, \cdot)\)	n/a	2688	6
5635.2.be	\(\chi_{5635}(804, \cdot)\)	n/a	4008	6
5635.2.bf	\(\chi_{5635}(484, \cdot)\)	n/a	3696	6
5635.2.bh	\(\chi_{5635}(576, \cdot)\)	n/a	4944	12
5635.2.bk	\(\chi_{5635}(636, \cdot)\)	n/a	3200	10
5635.2.bm	\(\chi_{5635}(244, \cdot)\)	n/a	4720	10
5635.2.bn	\(\chi_{5635}(834, \cdot)\)	n/a	4820	10
5635.2.bq	\(\chi_{5635}(22, \cdot)\)	n/a	8016	12
5635.2.br	\(\chi_{5635}(622, \cdot)\)	n/a	7392	12
5635.2.bt	\(\chi_{5635}(361, \cdot)\)	n/a	6400	20
5635.2.bv	\(\chi_{5635}(254, \cdot)\)	n/a	7392	12
5635.2.bw	\(\chi_{5635}(229, \cdot)\)	n/a	8016	12
5635.2.by	\(\chi_{5635}(206, \cdot)\)	n/a	5376	12
5635.2.cc	\(\chi_{5635}(148, \cdot)\)	n/a	9640	20
5635.2.cd	\(\chi_{5635}(48, \cdot)\)	n/a	9440	20
5635.2.cg	\(\chi_{5635}(324, \cdot)\)	n/a	9440	20
5635.2.ch	\(\chi_{5635}(19, \cdot)\)	n/a	9440	20
5635.2.cj	\(\chi_{5635}(166, \cdot)\)	n/a	6400	20
5635.2.cm	\(\chi_{5635}(36, \cdot)\)	n/a	26880	60
5635.2.cn	\(\chi_{5635}(137, \cdot)\)	n/a	16032	24
5635.2.cq	\(\chi_{5635}(47, \cdot)\)	n/a	14784	24
5635.2.cr	\(\chi_{5635}(67, \cdot)\)	n/a	18880	40
5635.2.cu	\(\chi_{5635}(117, \cdot)\)	n/a	18880	40
5635.2.cw	\(\chi_{5635}(29, \cdot)\)	n/a	40080	60
5635.2.cx	\(\chi_{5635}(34, \cdot)\)	n/a	40080	60
5635.2.cz	\(\chi_{5635}(76, \cdot)\)	n/a	26880	60
5635.2.dc	\(\chi_{5635}(16, \cdot)\)	n/a	53760	120
5635.2.de	\(\chi_{5635}(13, \cdot)\)	n/a	80160	120
5635.2.df	\(\chi_{5635}(43, \cdot)\)	n/a	80160	120
5635.2.dj	\(\chi_{5635}(61, \cdot)\)	n/a	53760	120
5635.2.dl	\(\chi_{5635}(89, \cdot)\)	n/a	80160	120
5635.2.dm	\(\chi_{5635}(4, \cdot)\)	n/a	80160	120
5635.2.do	\(\chi_{5635}(3, \cdot)\)	n/a	160320	240
5635.2.dr	\(\chi_{5635}(37, \cdot)\)	n/a	160320	240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5635))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5635)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1127))\)\(^{\oplus 2}\)