Space of modular forms of level 5782 and weight 2

• Label: 5782.2
• Level: 5782
• Weight: 2
• Dimension: 327075
• Nonzero newspaces: 16
• Sturm bound: 4092480

Defining parameters

Level:	\( N \)	=	\( 5782 = 2 \cdot 7^{2} \cdot 59 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(4092480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5782))\).

	Total	New	Old
Modular forms	1030080	327075	703005
Cusp forms	1016161	327075	689086
Eisenstein series	13919	0	13919

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5782))\)

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
5782.2.a	\(\chi_{5782}(1, \cdot)\)	5782.2.a.a	1	1
		5782.2.a.b	1
		5782.2.a.c	1
		5782.2.a.d	1
		5782.2.a.e	1
		5782.2.a.f	1
		5782.2.a.g	1
		5782.2.a.h	1
		5782.2.a.i	1
		5782.2.a.j	1
		5782.2.a.k	2
		5782.2.a.l	2
		5782.2.a.m	2
		5782.2.a.n	2
		5782.2.a.o	2
		5782.2.a.p	2
		5782.2.a.q	4
		5782.2.a.r	4
		5782.2.a.s	5
		5782.2.a.t	6
		5782.2.a.u	6
		5782.2.a.v	6
		5782.2.a.w	7
		5782.2.a.x	7
		5782.2.a.y	8
		5782.2.a.z	8
		5782.2.a.ba	10
		5782.2.a.bb	10
		5782.2.a.bc	10
		5782.2.a.bd	10
		5782.2.a.be	12
		5782.2.a.bf	12
		5782.2.a.bg	12
		5782.2.a.bh	12
		5782.2.a.bi	14
		5782.2.a.bj	14
5782.2.b	\(\chi_{5782}(5781, \cdot)\)	n/a	200	1
5782.2.e	\(\chi_{5782}(2125, \cdot)\)	n/a	384	2
5782.2.h	\(\chi_{5782}(117, \cdot)\)	n/a	400	2
5782.2.i	\(\chi_{5782}(827, \cdot)\)	n/a	1608	6
5782.2.l	\(\chi_{5782}(825, \cdot)\)	n/a	1680	6
5782.2.m	\(\chi_{5782}(473, \cdot)\)	n/a	3264	12
5782.2.n	\(\chi_{5782}(197, \cdot)\)	n/a	5740	28
5782.2.o	\(\chi_{5782}(353, \cdot)\)	n/a	3360	12
5782.2.t	\(\chi_{5782}(97, \cdot)\)	n/a	5600	28
5782.2.u	\(\chi_{5782}(79, \cdot)\)	n/a	11200	56
5782.2.v	\(\chi_{5782}(31, \cdot)\)	n/a	11200	56
5782.2.y	\(\chi_{5782}(15, \cdot)\)	n/a	47040	168
5782.2.z	\(\chi_{5782}(13, \cdot)\)	n/a	47040	168
5782.2.bc	\(\chi_{5782}(9, \cdot)\)	n/a	94080	336
5782.2.bf	\(\chi_{5782}(33, \cdot)\)	n/a	94080	336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5782))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5782)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(413))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(826))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2891))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5782))\)\(^{\oplus 1}\)