Space of modular forms of level 8022 and weight 2

• Label: 8022.2
• Level: 8022
• Weight: 2
• Dimension: 419493
• Nonzero newspaces: 32
• Sturm bound: 7004160

Defining parameters

Level:	\( N \)	=	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(7004160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8022))\).

	Total	New	Old
Modular forms	1760160	419493	1340667
Cusp forms	1741921	419493	1322428
Eisenstein series	18239	0	18239

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8022))\)

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
8022.2.a	\(\chi_{8022}(1, \cdot)\)	8022.2.a.a	1	1
		8022.2.a.b	1
		8022.2.a.c	1
		8022.2.a.d	1
		8022.2.a.e	1
		8022.2.a.f	1
		8022.2.a.g	1
		8022.2.a.h	1
		8022.2.a.i	1
		8022.2.a.j	2
		8022.2.a.k	2
		8022.2.a.l	7
		8022.2.a.m	7
		8022.2.a.n	8
		8022.2.a.o	8
		8022.2.a.p	9
		8022.2.a.q	9
		8022.2.a.r	10
		8022.2.a.s	11
		8022.2.a.t	11
		8022.2.a.u	11
		8022.2.a.v	13
		8022.2.a.w	13
		8022.2.a.x	14
		8022.2.a.y	14
		8022.2.a.z	15
		8022.2.a.ba	16
8022.2.b	\(\chi_{8022}(5347, \cdot)\)	n/a	256	1
8022.2.e	\(\chi_{8022}(6875, \cdot)\)	n/a	384	1
8022.2.f	\(\chi_{8022}(3821, \cdot)\)	n/a	504	1
8022.2.i	\(\chi_{8022}(2293, \cdot)\)	n/a	504	2
8022.2.j	\(\chi_{8022}(421, \cdot)\)	n/a	768	4
8022.2.l	\(\chi_{8022}(383, \cdot)\)	n/a	1016	2
8022.2.o	\(\chi_{8022}(1145, \cdot)\)	n/a	1024	2
8022.2.p	\(\chi_{8022}(1909, \cdot)\)	n/a	512	2
8022.2.s	\(\chi_{8022}(1861, \cdot)\)	n/a	1024	4
8022.2.t	\(\chi_{8022}(1037, \cdot)\)	n/a	1536	4
8022.2.w	\(\chi_{8022}(1637, \cdot)\)	n/a	2048	4
8022.2.y	\(\chi_{8022}(109, \cdot)\)	n/a	2048	8
8022.2.z	\(\chi_{8022}(1135, \cdot)\)	n/a	3456	18
8022.2.bc	\(\chi_{8022}(803, \cdot)\)	n/a	4096	8
8022.2.bd	\(\chi_{8022}(389, \cdot)\)	n/a	4096	8
8022.2.bg	\(\chi_{8022}(1153, \cdot)\)	n/a	2048	8
8022.2.bj	\(\chi_{8022}(125, \cdot)\)	n/a	9216	18
8022.2.bk	\(\chi_{8022}(155, \cdot)\)	n/a	6912	18
8022.2.bn	\(\chi_{8022}(55, \cdot)\)	n/a	4608	18
8022.2.bo	\(\chi_{8022}(25, \cdot)\)	n/a	9216	36
8022.2.bp	\(\chi_{8022}(43, \cdot)\)	n/a	13824	72
8022.2.br	\(\chi_{8022}(31, \cdot)\)	n/a	9216	36
8022.2.bs	\(\chi_{8022}(11, \cdot)\)	n/a	18432	36
8022.2.bv	\(\chi_{8022}(5, \cdot)\)	n/a	18432	36
8022.2.by	\(\chi_{8022}(209, \cdot)\)	n/a	36864	72
8022.2.cb	\(\chi_{8022}(29, \cdot)\)	n/a	27648	72
8022.2.cc	\(\chi_{8022}(181, \cdot)\)	n/a	18432	72
8022.2.ce	\(\chi_{8022}(67, \cdot)\)	n/a	36864	144
8022.2.cf	\(\chi_{8022}(19, \cdot)\)	n/a	36864	144
8022.2.ci	\(\chi_{8022}(53, \cdot)\)	n/a	73728	144
8022.2.cj	\(\chi_{8022}(17, \cdot)\)	n/a	73728	144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(191))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(382))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(573))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1146))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1337))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2674))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4011))\)\(^{\oplus 2}\)