Space of modular forms of level 6016 and weight 2

• Label: 6016.2
• Level: 6016
• Weight: 2
• Dimension: 633168
• Nonzero newspaces: 20
• Sturm bound: 4521984

Defining parameters

Level:	\( N \)	=	\( 6016 = 2^{7} \cdot 47 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(4521984\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6016))\).

	Total	New	Old
Modular forms	1137856	637488	500368
Cusp forms	1123137	633168	489969
Eisenstein series	14719	4320	10399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6016))\)

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
6016.2.a	\(\chi_{6016}(1, \cdot)\)	6016.2.a.a	1	1
		6016.2.a.b	1
		6016.2.a.c	1
		6016.2.a.d	1
		6016.2.a.e	8
		6016.2.a.f	8
		6016.2.a.g	8
		6016.2.a.h	8
		6016.2.a.i	10
		6016.2.a.j	10
		6016.2.a.k	10
		6016.2.a.l	10
		6016.2.a.m	13
		6016.2.a.n	13
		6016.2.a.o	13
		6016.2.a.p	13
		6016.2.a.q	14
		6016.2.a.r	14
		6016.2.a.s	14
		6016.2.a.t	14
6016.2.b	\(\chi_{6016}(6015, \cdot)\)	n/a	192	1
6016.2.c	\(\chi_{6016}(3009, \cdot)\)	n/a	184	1
6016.2.h	\(\chi_{6016}(3007, \cdot)\)	n/a	192	1
6016.2.j	\(\chi_{6016}(1505, \cdot)\)	n/a	368	2
6016.2.l	\(\chi_{6016}(1503, \cdot)\)	n/a	376	2
6016.2.m	\(\chi_{6016}(751, \cdot)\)	n/a	760	4
6016.2.n	\(\chi_{6016}(753, \cdot)\)	n/a	736	4
6016.2.q	\(\chi_{6016}(377, \cdot)\)	None	0	8
6016.2.r	\(\chi_{6016}(375, \cdot)\)	None	0	8
6016.2.u	\(\chi_{6016}(385, \cdot)\)	n/a	4224	22
6016.2.w	\(\chi_{6016}(189, \cdot)\)	n/a	11776	16
6016.2.y	\(\chi_{6016}(187, \cdot)\)	n/a	12256	16
6016.2.z	\(\chi_{6016}(575, \cdot)\)	n/a	4224	22
6016.2.be	\(\chi_{6016}(65, \cdot)\)	n/a	4224	22
6016.2.bf	\(\chi_{6016}(127, \cdot)\)	n/a	4224	22
6016.2.bg	\(\chi_{6016}(31, \cdot)\)	n/a	8272	44
6016.2.bi	\(\chi_{6016}(97, \cdot)\)	n/a	8272	44
6016.2.bm	\(\chi_{6016}(17, \cdot)\)	n/a	16720	88
6016.2.bn	\(\chi_{6016}(15, \cdot)\)	n/a	16720	88
6016.2.bq	\(\chi_{6016}(23, \cdot)\)	None	0	176
6016.2.br	\(\chi_{6016}(9, \cdot)\)	None	0	176
6016.2.bs	\(\chi_{6016}(11, \cdot)\)	n/a	269632	352
6016.2.bu	\(\chi_{6016}(21, \cdot)\)	n/a	269632	352

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(94))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(188))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(376))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(752))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3008))\)\(^{\oplus 2}\)