Space of modular forms of level 5766 and weight 2

• Label: 5766.2
• Level: 5766
• Weight: 2
• Dimension: 230159
• Nonzero newspaces: 16
• Sturm bound: 3690240

Defining parameters

Level:	\( N \)	=	\( 5766 = 2 \cdot 3 \cdot 31^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(3690240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5766))\).

	Total	New	Old
Modular forms	928080	230159	697921
Cusp forms	917041	230159	686882
Eisenstein series	11039	0	11039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5766))\)

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
5766.2.a	\(\chi_{5766}(1, \cdot)\)	5766.2.a.a	1	1
		5766.2.a.b	1
		5766.2.a.c	1
		5766.2.a.d	1
		5766.2.a.e	1
		5766.2.a.f	1
		5766.2.a.g	1
		5766.2.a.h	1
		5766.2.a.i	1
		5766.2.a.j	2
		5766.2.a.k	2
		5766.2.a.l	2
		5766.2.a.m	2
		5766.2.a.n	2
		5766.2.a.o	2
		5766.2.a.p	2
		5766.2.a.q	2
		5766.2.a.r	2
		5766.2.a.s	2
		5766.2.a.t	2
		5766.2.a.u	2
		5766.2.a.v	2
		5766.2.a.w	4
		5766.2.a.x	4
		5766.2.a.y	4
		5766.2.a.z	4
		5766.2.a.ba	4
		5766.2.a.bb	4
		5766.2.a.bc	4
		5766.2.a.bd	4
		5766.2.a.be	4
		5766.2.a.bf	4
		5766.2.a.bg	4
		5766.2.a.bh	4
		5766.2.a.bi	4
		5766.2.a.bj	4
		5766.2.a.bk	8
		5766.2.a.bl	8
		5766.2.a.bm	8
		5766.2.a.bn	8
		5766.2.a.bo	8
		5766.2.a.bp	8
		5766.2.a.bq	8
		5766.2.a.br	8
5766.2.c	\(\chi_{5766}(5765, \cdot)\)	n/a	308	1
5766.2.e	\(\chi_{5766}(439, \cdot)\)	n/a	308	2
5766.2.f	\(\chi_{5766}(3271, \cdot)\)	n/a	624	4
5766.2.h	\(\chi_{5766}(3323, \cdot)\)	n/a	620	2
5766.2.j	\(\chi_{5766}(587, \cdot)\)	n/a	1232	4
5766.2.m	\(\chi_{5766}(235, \cdot)\)	n/a	1232	8
5766.2.p	\(\chi_{5766}(623, \cdot)\)	n/a	2480	8
5766.2.q	\(\chi_{5766}(187, \cdot)\)	n/a	4920	30
5766.2.s	\(\chi_{5766}(185, \cdot)\)	n/a	9960	30
5766.2.u	\(\chi_{5766}(25, \cdot)\)	n/a	9960	60
5766.2.v	\(\chi_{5766}(97, \cdot)\)	n/a	19680	120
5766.2.x	\(\chi_{5766}(119, \cdot)\)	n/a	19800	60
5766.2.bb	\(\chi_{5766}(23, \cdot)\)	n/a	39840	120
5766.2.bc	\(\chi_{5766}(7, \cdot)\)	n/a	39840	240
5766.2.bd	\(\chi_{5766}(11, \cdot)\)	n/a	79200	240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5766))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5766)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1922))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2883))\)\(^{\oplus 2}\)