Space of modular forms of level 9537 and weight 2

• Label: 9537.2
• Level: 9537
• Weight: 2
• Dimension: 2431746
• Nonzero newspaces: 40
• Sturm bound: 13317120

Defining parameters

Level:	\( N \)	=	\( 9537 = 3 \cdot 11 \cdot 17^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(13317120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9537))\).

	Total	New	Old
Modular forms	3345280	2445014	900266
Cusp forms	3313281	2431746	881535
Eisenstein series	31999	13268	18731

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9537))\)

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
9537.2.a	\(\chi_{9537}(1, \cdot)\)	9537.2.a.a	1	1
		9537.2.a.b	1
		9537.2.a.c	1
		9537.2.a.d	1
		9537.2.a.e	1
		9537.2.a.f	1
		9537.2.a.g	1
		9537.2.a.h	1
		9537.2.a.i	1
		9537.2.a.j	1
		9537.2.a.k	1
		9537.2.a.l	1
		9537.2.a.m	1
		9537.2.a.n	2
		9537.2.a.o	2
		9537.2.a.p	2
		9537.2.a.q	2
		9537.2.a.r	2
		9537.2.a.s	2
		9537.2.a.t	2
		9537.2.a.u	2
		9537.2.a.v	3
		9537.2.a.w	3
		9537.2.a.x	3
		9537.2.a.y	4
		9537.2.a.z	5
		9537.2.a.ba	5
		9537.2.a.bb	5
		9537.2.a.bc	5
		9537.2.a.bd	6
		9537.2.a.be	6
		9537.2.a.bf	6
		9537.2.a.bg	6
		9537.2.a.bh	6
		9537.2.a.bi	6
		9537.2.a.bj	6
		9537.2.a.bk	6
		9537.2.a.bl	6
		9537.2.a.bm	8
		9537.2.a.bn	8
		9537.2.a.bo	10
		9537.2.a.bp	10
		9537.2.a.bq	14
		9537.2.a.br	14
		9537.2.a.bs	15
		9537.2.a.bt	15
		9537.2.a.bu	18
		9537.2.a.bv	18
		9537.2.a.bw	18
		9537.2.a.bx	18
		9537.2.a.by	21
		9537.2.a.bz	21
		9537.2.a.ca	28
		9537.2.a.cb	28
		9537.2.a.cc	36
		9537.2.a.cd	36
9537.2.f	\(\chi_{9537}(7226, \cdot)\)	n/a	1054	1
9537.2.g	\(\chi_{9537}(2311, \cdot)\)	n/a	452	1
9537.2.h	\(\chi_{9537}(9536, \cdot)\)	n/a	1052	1
9537.2.i	\(\chi_{9537}(2639, \cdot)\)	n/a	2104	2
9537.2.j	\(\chi_{9537}(4951, \cdot)\)	n/a	904	2
9537.2.m	\(\chi_{9537}(3469, \cdot)\)	n/a	2168	4
9537.2.o	\(\chi_{9537}(3334, \cdot)\)	n/a	1792	4
9537.2.q	\(\chi_{9537}(1022, \cdot)\)	n/a	4208	4
9537.2.r	\(\chi_{9537}(866, \cdot)\)	n/a	4208	4
9537.2.s	\(\chi_{9537}(577, \cdot)\)	n/a	2160	4
9537.2.t	\(\chi_{9537}(1157, \cdot)\)	n/a	4216	4
9537.2.y	\(\chi_{9537}(538, \cdot)\)	n/a	4320	8
9537.2.z	\(\chi_{9537}(6029, \cdot)\)	n/a	7200	8
9537.2.bc	\(\chi_{9537}(562, \cdot)\)	n/a	8128	16
9537.2.bf	\(\chi_{9537}(829, \cdot)\)	n/a	4320	8
9537.2.bg	\(\chi_{9537}(1118, \cdot)\)	n/a	8416	8
9537.2.bh	\(\chi_{9537}(560, \cdot)\)	n/a	19520	16
9537.2.bi	\(\chi_{9537}(67, \cdot)\)	n/a	8128	16
9537.2.bj	\(\chi_{9537}(494, \cdot)\)	n/a	19520	16
9537.2.bo	\(\chi_{9537}(134, \cdot)\)	n/a	16832	16
9537.2.bq	\(\chi_{9537}(757, \cdot)\)	n/a	8640	16
9537.2.bu	\(\chi_{9537}(166, \cdot)\)	n/a	16256	32
9537.2.bv	\(\chi_{9537}(98, \cdot)\)	n/a	39040	32
9537.2.by	\(\chi_{9537}(158, \cdot)\)	n/a	33664	32
9537.2.bz	\(\chi_{9537}(40, \cdot)\)	n/a	17280	32
9537.2.ca	\(\chi_{9537}(103, \cdot)\)	n/a	39168	64
9537.2.cb	\(\chi_{9537}(32, \cdot)\)	n/a	78080	64
9537.2.cd	\(\chi_{9537}(100, \cdot)\)	n/a	32768	64
9537.2.cj	\(\chi_{9537}(35, \cdot)\)	n/a	78080	64
9537.2.ck	\(\chi_{9537}(16, \cdot)\)	n/a	39168	64
9537.2.cl	\(\chi_{9537}(50, \cdot)\)	n/a	78080	64
9537.2.co	\(\chi_{9537}(23, \cdot)\)	n/a	130560	128
9537.2.cp	\(\chi_{9537}(10, \cdot)\)	n/a	78336	128
9537.2.cq	\(\chi_{9537}(140, \cdot)\)	n/a	156160	128
9537.2.cr	\(\chi_{9537}(4, \cdot)\)	n/a	78336	128
9537.2.cv	\(\chi_{9537}(25, \cdot)\)	n/a	156672	256
9537.2.cx	\(\chi_{9537}(2, \cdot)\)	n/a	312320	256
9537.2.cy	\(\chi_{9537}(7, \cdot)\)	n/a	313344	512
9537.2.cz	\(\chi_{9537}(5, \cdot)\)	n/a	624640	512

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9537))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9537)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3179))\)\(^{\oplus 2}\)