Space of modular forms of level 9801 and weight 2

• Label: 9801.2
• Level: 9801
• Weight: 2
• Dimension: 2734084
• Nonzero newspaces: 32
• Sturm bound: 14113440

Defining parameters

Level:	\( N \)	=	\( 9801 = 3^{4} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(14113440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9801))\).

	Total	New	Old
Modular forms	3545640	2749820	795820
Cusp forms	3511081	2734084	776997
Eisenstein series	34559	15736	18823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9801))\)

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
9801.2.a	\(\chi_{9801}(1, \cdot)\)	9801.2.a.a	1	1
		9801.2.a.b	1
		9801.2.a.c	1
		9801.2.a.d	1
		9801.2.a.e	1
		9801.2.a.f	1
		9801.2.a.g	1
		9801.2.a.h	1
		9801.2.a.i	1
		9801.2.a.j	1
		9801.2.a.k	1
		9801.2.a.l	1
		9801.2.a.m	2
		9801.2.a.n	2
		9801.2.a.o	2
		9801.2.a.p	2
		9801.2.a.q	2
		9801.2.a.r	2
		9801.2.a.s	2
		9801.2.a.t	2
		9801.2.a.u	2
		9801.2.a.v	2
		9801.2.a.w	2
		9801.2.a.x	2
		9801.2.a.y	2
		9801.2.a.z	2
		9801.2.a.ba	2
		9801.2.a.bb	2
		9801.2.a.bc	2
		9801.2.a.bd	3
		9801.2.a.be	3
		9801.2.a.bf	3
		9801.2.a.bg	3
		9801.2.a.bh	4
		9801.2.a.bi	4
		9801.2.a.bj	4
		9801.2.a.bk	4
		9801.2.a.bl	4
		9801.2.a.bm	4
		9801.2.a.bn	5
		9801.2.a.bo	5
		9801.2.a.bp	5
		9801.2.a.bq	5
		9801.2.a.br	6
		9801.2.a.bs	6
		9801.2.a.bt	6
		9801.2.a.bu	6
		9801.2.a.bv	8
		9801.2.a.bw	8
		9801.2.a.bx	8
		9801.2.a.by	8
		9801.2.a.bz	8
		9801.2.a.ca	8
		9801.2.a.cb	10
		9801.2.a.cc	10
		9801.2.a.cd	10
		9801.2.a.ce	10
		9801.2.a.cf	12
		9801.2.a.cg	12
		9801.2.a.ch	12
		9801.2.a.ci	12
		9801.2.a.cj	12
		9801.2.a.ck	12
		9801.2.a.cl	12
9801.2.a.cm	18
9801.2.a.cn	18
9801.2.a.co	18
9801.2.a.cp	18
9801.2.a.cq	24
9801.2.a.cr	24
9801.2.d	\(\chi_{9801}(9800, \cdot)\)	n/a	416	1
9801.2.e	\(\chi_{9801}(3268, \cdot)\)	n/a	854	2
9801.2.f	\(\chi_{9801}(487, \cdot)\)	n/a	1664	4
9801.2.g	\(\chi_{9801}(3266, \cdot)\)	n/a	848	2
9801.2.j	\(\chi_{9801}(1090, \cdot)\)	n/a	1908	6
9801.2.k	\(\chi_{9801}(161, \cdot)\)	n/a	1664	4
9801.2.n	\(\chi_{9801}(892, \cdot)\)	n/a	5240	10
9801.2.o	\(\chi_{9801}(3052, \cdot)\)	n/a	3392	8
9801.2.p	\(\chi_{9801}(1088, \cdot)\)	n/a	1896	6
9801.2.s	\(\chi_{9801}(890, \cdot)\)	n/a	5240	10
9801.2.v	\(\chi_{9801}(364, \cdot)\)	n/a	17496	18
9801.2.y	\(\chi_{9801}(215, \cdot)\)	n/a	3392	8
9801.2.z	\(\chi_{9801}(298, \cdot)\)	n/a	10520	20
9801.2.ba	\(\chi_{9801}(856, \cdot)\)	n/a	7584	24
9801.2.bd	\(\chi_{9801}(362, \cdot)\)	n/a	17352	18
9801.2.be	\(\chi_{9801}(82, \cdot)\)	n/a	20960	40
9801.2.bh	\(\chi_{9801}(296, \cdot)\)	n/a	10520	20
9801.2.bk	\(\chi_{9801}(233, \cdot)\)	n/a	7584	24
9801.2.bl	\(\chi_{9801}(100, \cdot)\)	n/a	23640	60
9801.2.bo	\(\chi_{9801}(404, \cdot)\)	n/a	20960	40
9801.2.bp	\(\chi_{9801}(124, \cdot)\)	n/a	69408	72
9801.2.bq	\(\chi_{9801}(136, \cdot)\)	n/a	42080	80
9801.2.bt	\(\chi_{9801}(98, \cdot)\)	n/a	23640	60
9801.2.bu	\(\chi_{9801}(239, \cdot)\)	n/a	69408	72
9801.2.bx	\(\chi_{9801}(34, \cdot)\)	n/a	213480	180
9801.2.by	\(\chi_{9801}(107, \cdot)\)	n/a	42080	80
9801.2.cb	\(\chi_{9801}(37, \cdot)\)	n/a	94560	240
9801.2.cc	\(\chi_{9801}(32, \cdot)\)	n/a	213480	180
9801.2.cf	\(\chi_{9801}(8, \cdot)\)	n/a	94560	240
9801.2.ci	\(\chi_{9801}(4, \cdot)\)	n/a	853920	720
9801.2.cl	\(\chi_{9801}(2, \cdot)\)	n/a	853920	720

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9801))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9801)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(891))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3267))\)\(^{\oplus 2}\)