Space of modular forms of level 8016 and weight 2

• Label: 8016.2
• Level: 8016
• Weight: 2
• Dimension: 751436
• Nonzero newspaces: 16
• Sturm bound: 7139328

Defining parameters

Level:	\( N \)	=	\( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(7139328\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8016))\).

	Total	New	Old
Modular forms	1794128	754408	1039720
Cusp forms	1775537	751436	1024101
Eisenstein series	18591	2972	15619

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8016))\)

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
8016.2.a	\(\chi_{8016}(1, \cdot)\)	8016.2.a.a	1	1
		8016.2.a.b	1
		8016.2.a.c	1
		8016.2.a.d	1
		8016.2.a.e	1
		8016.2.a.f	1
		8016.2.a.g	1
		8016.2.a.h	1
		8016.2.a.i	1
		8016.2.a.j	1
		8016.2.a.k	2
		8016.2.a.l	3
		8016.2.a.m	3
		8016.2.a.n	3
		8016.2.a.o	4
		8016.2.a.p	5
		8016.2.a.q	5
		8016.2.a.r	5
		8016.2.a.s	5
		8016.2.a.t	5
		8016.2.a.u	5
		8016.2.a.v	7
		8016.2.a.w	7
		8016.2.a.x	8
		8016.2.a.y	8
		8016.2.a.z	8
		8016.2.a.ba	9
		8016.2.a.bb	9
		8016.2.a.bc	9
		8016.2.a.bd	10
		8016.2.a.be	11
		8016.2.a.bf	12
		8016.2.a.bg	13
8016.2.b	\(\chi_{8016}(2671, \cdot)\)	n/a	168	1
8016.2.e	\(\chi_{8016}(335, \cdot)\)	n/a	332	1
8016.2.f	\(\chi_{8016}(4009, \cdot)\)	None	0	1
8016.2.i	\(\chi_{8016}(1001, \cdot)\)	None	0	1
8016.2.j	\(\chi_{8016}(4343, \cdot)\)	None	0	1
8016.2.m	\(\chi_{8016}(6679, \cdot)\)	None	0	1
8016.2.n	\(\chi_{8016}(5009, \cdot)\)	n/a	334	1
8016.2.s	\(\chi_{8016}(3005, \cdot)\)	n/a	2680	2
8016.2.t	\(\chi_{8016}(2005, \cdot)\)	n/a	1328	2
8016.2.u	\(\chi_{8016}(667, \cdot)\)	n/a	1344	2
8016.2.v	\(\chi_{8016}(2339, \cdot)\)	n/a	2656	2
8016.2.y	\(\chi_{8016}(49, \cdot)\)	n/a	13776	82
8016.2.bb	\(\chi_{8016}(17, \cdot)\)	n/a	27388	82
8016.2.bc	\(\chi_{8016}(55, \cdot)\)	None	0	82
8016.2.bf	\(\chi_{8016}(215, \cdot)\)	None	0	82
8016.2.bg	\(\chi_{8016}(41, \cdot)\)	None	0	82
8016.2.bj	\(\chi_{8016}(25, \cdot)\)	None	0	82
8016.2.bk	\(\chi_{8016}(47, \cdot)\)	n/a	27552	82
8016.2.bn	\(\chi_{8016}(79, \cdot)\)	n/a	13776	82
8016.2.bq	\(\chi_{8016}(11, \cdot)\)	n/a	219760	164
8016.2.br	\(\chi_{8016}(43, \cdot)\)	n/a	110208	164
8016.2.bs	\(\chi_{8016}(61, \cdot)\)	n/a	110208	164
8016.2.bt	\(\chi_{8016}(5, \cdot)\)	n/a	219760	164

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4008))\)\(^{\oplus 2}\)