Space of modular forms of level 8281 and weight 2

• Label: 8281.2
• Level: 8281
• Weight: 2
• Dimension: 2628608
• Nonzero newspaces: 60
• Sturm bound: 11129664

Defining parameters

Level:	\( N \)	=	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(11129664\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8281))\).

	Total	New	Old
Modular forms	2796096	2648445	147651
Cusp forms	2768737	2628608	140129
Eisenstein series	27359	19837	7522

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8281))\)

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
8281.2.a	\(\chi_{8281}(1, \cdot)\)	8281.2.a.a	1	1
		8281.2.a.b	1
		8281.2.a.c	1
		8281.2.a.d	1
		8281.2.a.e	1
		8281.2.a.f	1
		8281.2.a.g	1
		8281.2.a.h	1
		8281.2.a.i	1
		8281.2.a.j	1
		8281.2.a.k	1
		8281.2.a.l	1
		8281.2.a.m	1
		8281.2.a.n	2
		8281.2.a.o	2
		8281.2.a.p	2
		8281.2.a.q	2
		8281.2.a.r	2
		8281.2.a.s	2
		8281.2.a.t	2
		8281.2.a.u	2
		8281.2.a.v	2
		8281.2.a.w	2
		8281.2.a.x	2
		8281.2.a.y	2
		8281.2.a.z	2
		8281.2.a.ba	2
		8281.2.a.bb	2
		8281.2.a.bc	3
		8281.2.a.bd	3
		8281.2.a.be	3
		8281.2.a.bf	3
		8281.2.a.bg	3
		8281.2.a.bh	3
		8281.2.a.bi	3
		8281.2.a.bj	3
		8281.2.a.bk	3
		8281.2.a.bl	3
		8281.2.a.bm	3
		8281.2.a.bn	4
		8281.2.a.bo	4
		8281.2.a.bp	4
		8281.2.a.bq	4
		8281.2.a.br	4
		8281.2.a.bs	4
		8281.2.a.bt	4
		8281.2.a.bu	4
		8281.2.a.bv	4
		8281.2.a.bw	5
		8281.2.a.bx	5
		8281.2.a.by	6
		8281.2.a.bz	6
		8281.2.a.ca	6
		8281.2.a.cb	6
		8281.2.a.cc	6
		8281.2.a.cd	6
		8281.2.a.ce	6
		8281.2.a.cf	6
		8281.2.a.cg	6
		8281.2.a.ch	6
		8281.2.a.ci	8
		8281.2.a.cj	8
		8281.2.a.ck	8
		8281.2.a.cl	8
8281.2.a.cm	12
8281.2.a.cn	12
8281.2.a.co	12
8281.2.a.cp	12
8281.2.a.cq	12
8281.2.a.cr	12
8281.2.a.cs	16
8281.2.a.ct	24
8281.2.a.cu	24
8281.2.a.cv	24
8281.2.a.cw	24
8281.2.a.cx	32
8281.2.a.cy	36
8281.2.a.cz	36
8281.2.c	\(\chi_{8281}(1520, \cdot)\)	n/a	500	1
8281.2.e	\(\chi_{8281}(508, \cdot)\)	n/a	990	2
8281.2.f	\(\chi_{8281}(1667, \cdot)\)	n/a	1004	2
8281.2.g	\(\chi_{8281}(2174, \cdot)\)	n/a	986	2
8281.2.h	\(\chi_{8281}(3019, \cdot)\)	n/a	986	2
8281.2.i	\(\chi_{8281}(6859, \cdot)\)	n/a	984	2
8281.2.k	\(\chi_{8281}(1206, \cdot)\)	n/a	986	2
8281.2.q	\(\chi_{8281}(5048, \cdot)\)	n/a	1002	2
8281.2.r	\(\chi_{8281}(2027, \cdot)\)	n/a	988	2
8281.2.u	\(\chi_{8281}(361, \cdot)\)	n/a	986	2
8281.2.w	\(\chi_{8281}(1184, \cdot)\)	n/a	4278	6
8281.2.x	\(\chi_{8281}(19, \cdot)\)	n/a	1972	4
8281.2.bb	\(\chi_{8281}(864, \cdot)\)	n/a	1972	4
8281.2.bc	\(\chi_{8281}(5507, \cdot)\)	n/a	1976	4
8281.2.bd	\(\chi_{8281}(587, \cdot)\)	n/a	1976	4
8281.2.bf	\(\chi_{8281}(638, \cdot)\)	n/a	7404	12
8281.2.bh	\(\chi_{8281}(337, \cdot)\)	n/a	4260	6
8281.2.bj	\(\chi_{8281}(529, \cdot)\)	n/a	8508	12
8281.2.bk	\(\chi_{8281}(191, \cdot)\)	n/a	8508	12
8281.2.bl	\(\chi_{8281}(22, \cdot)\)	n/a	8496	12
8281.2.bm	\(\chi_{8281}(170, \cdot)\)	n/a	8544	12
8281.2.bo	\(\chi_{8281}(246, \cdot)\)	n/a	7416	12
8281.2.br	\(\chi_{8281}(944, \cdot)\)	n/a	8520	12
8281.2.bs	\(\chi_{8281}(165, \cdot)\)	n/a	14472	24
8281.2.bt	\(\chi_{8281}(263, \cdot)\)	n/a	14472	24
8281.2.bu	\(\chi_{8281}(295, \cdot)\)	n/a	14784	24
8281.2.bv	\(\chi_{8281}(79, \cdot)\)	n/a	14448	24
8281.2.bx	\(\chi_{8281}(485, \cdot)\)	n/a	8508	12
8281.2.ca	\(\chi_{8281}(506, \cdot)\)	n/a	8496	12
8281.2.cb	\(\chi_{8281}(316, \cdot)\)	n/a	8496	12
8281.2.ch	\(\chi_{8281}(23, \cdot)\)	n/a	8508	12
8281.2.cj	\(\chi_{8281}(489, \cdot)\)	n/a	14496	24
8281.2.cl	\(\chi_{8281}(30, \cdot)\)	n/a	14472	24
8281.2.co	\(\chi_{8281}(116, \cdot)\)	n/a	14448	24
8281.2.cp	\(\chi_{8281}(491, \cdot)\)	n/a	14808	24
8281.2.cv	\(\chi_{8281}(459, \cdot)\)	n/a	14472	24
8281.2.cx	\(\chi_{8281}(188, \cdot)\)	n/a	16992	24
8281.2.cy	\(\chi_{8281}(437, \cdot)\)	n/a	16992	24
8281.2.cz	\(\chi_{8281}(89, \cdot)\)	n/a	17016	24
8281.2.dd	\(\chi_{8281}(488, \cdot)\)	n/a	17016	24
8281.2.de	\(\chi_{8281}(92, \cdot)\)	n/a	60912	72
8281.2.dg	\(\chi_{8281}(97, \cdot)\)	n/a	28896	48
8281.2.dh	\(\chi_{8281}(31, \cdot)\)	n/a	28896	48
8281.2.di	\(\chi_{8281}(227, \cdot)\)	n/a	28944	48
8281.2.dm	\(\chi_{8281}(215, \cdot)\)	n/a	28944	48
8281.2.do	\(\chi_{8281}(64, \cdot)\)	n/a	60912	72
8281.2.dq	\(\chi_{8281}(53, \cdot)\)	n/a	122112	144
8281.2.dr	\(\chi_{8281}(29, \cdot)\)	n/a	122112	144
8281.2.ds	\(\chi_{8281}(9, \cdot)\)	n/a	121968	144
8281.2.dt	\(\chi_{8281}(16, \cdot)\)	n/a	121968	144
8281.2.du	\(\chi_{8281}(34, \cdot)\)	n/a	121824	144
8281.2.dw	\(\chi_{8281}(4, \cdot)\)	n/a	121968	144
8281.2.ec	\(\chi_{8281}(36, \cdot)\)	n/a	122112	144
8281.2.ed	\(\chi_{8281}(25, \cdot)\)	n/a	122112	144
8281.2.eg	\(\chi_{8281}(88, \cdot)\)	n/a	121968	144
8281.2.ei	\(\chi_{8281}(24, \cdot)\)	n/a	243936	288
8281.2.em	\(\chi_{8281}(45, \cdot)\)	n/a	243936	288
8281.2.en	\(\chi_{8281}(5, \cdot)\)	n/a	244224	288
8281.2.eo	\(\chi_{8281}(6, \cdot)\)	n/a	244224	288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8281))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8281)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)