Space of modular forms of level 7803 and weight 2

• Label: 7803.2
• Level: 7803
• Weight: 2
• Dimension: 1757453
• Nonzero newspaces: 30
• Sturm bound: 8989056

Defining parameters

Level:	\( N \)	=	\( 7803 = 3^{3} \cdot 17^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(8989056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7803))\).

	Total	New	Old
Modular forms	2259264	1769245	490019
Cusp forms	2235265	1757453	477812
Eisenstein series	23999	11792	12207

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7803))\)

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 the newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
7803.2.a	\(\chi_{7803}(1, \cdot)\)	7803.2.a.a	1	1
		7803.2.a.b	1
		7803.2.a.c	1
		7803.2.a.d	1
		7803.2.a.e	1
		7803.2.a.f	1
		7803.2.a.g	1
		7803.2.a.h	1
		7803.2.a.i	1
		7803.2.a.j	1
		7803.2.a.k	1
		7803.2.a.l	1
		7803.2.a.m	1
		7803.2.a.n	1
		7803.2.a.o	1
		7803.2.a.p	1
		7803.2.a.q	1
		7803.2.a.r	1
		7803.2.a.s	1
		7803.2.a.t	1
		7803.2.a.u	1
		7803.2.a.v	2
		7803.2.a.w	2
		7803.2.a.x	2
		7803.2.a.y	2
		7803.2.a.z	2
		7803.2.a.ba	2
		7803.2.a.bb	2
		7803.2.a.bc	2
		7803.2.a.bd	3
		7803.2.a.be	3
		7803.2.a.bf	3
		7803.2.a.bg	3
		7803.2.a.bh	4
		7803.2.a.bi	4
		7803.2.a.bj	5
		7803.2.a.bk	5
		7803.2.a.bl	5
		7803.2.a.bm	5
		7803.2.a.bn	6
		7803.2.a.bo	6
		7803.2.a.bp	6
		7803.2.a.bq	6
		7803.2.a.br	10
		7803.2.a.bs	10
		7803.2.a.bt	12
		7803.2.a.bu	12
		7803.2.a.bv	12
		7803.2.a.bw	12
		7803.2.a.bx	15
		7803.2.a.by	15
		7803.2.a.bz	15
		7803.2.a.ca	15
		7803.2.a.cb	18
		7803.2.a.cc	18
		7803.2.a.cd	24
		7803.2.a.ce	24
		7803.2.a.cf	24
		7803.2.a.cg	24
7803.2.d	\(\chi_{7803}(5779, \cdot)\)	n/a	360	1
7803.2.e	\(\chi_{7803}(2602, \cdot)\)	n/a	512	2
7803.2.f	\(\chi_{7803}(2350, \cdot)\)	n/a	720	2
7803.2.h	\(\chi_{7803}(577, \cdot)\)	n/a	512	2
7803.2.l	\(\chi_{7803}(757, \cdot)\)	n/a	1440	4
7803.2.m	\(\chi_{7803}(868, \cdot)\)	n/a	4788	6
7803.2.o	\(\chi_{7803}(829, \cdot)\)	n/a	1024	4
7803.2.p	\(\chi_{7803}(998, \cdot)\)	n/a	2880	8
7803.2.r	\(\chi_{7803}(460, \cdot)\)	n/a	6528	16
7803.2.s	\(\chi_{7803}(1444, \cdot)\)	n/a	4776	6
7803.2.w	\(\chi_{7803}(712, \cdot)\)	n/a	2048	8
7803.2.x	\(\chi_{7803}(271, \cdot)\)	n/a	6528	16
7803.2.bb	\(\chi_{7803}(616, \cdot)\)	n/a	9552	12
7803.2.bc	\(\chi_{7803}(224, \cdot)\)	n/a	4096	16
7803.2.be	\(\chi_{7803}(154, \cdot)\)	n/a	9728	32
7803.2.bg	\(\chi_{7803}(55, \cdot)\)	n/a	13056	32
7803.2.bh	\(\chi_{7803}(688, \cdot)\)	n/a	19104	24
7803.2.bl	\(\chi_{7803}(118, \cdot)\)	n/a	9728	32
7803.2.bm	\(\chi_{7803}(298, \cdot)\)	n/a	26112	64
7803.2.bp	\(\chi_{7803}(65, \cdot)\)	n/a	38208	48
7803.2.bq	\(\chi_{7803}(52, \cdot)\)	n/a	87936	96
7803.2.br	\(\chi_{7803}(64, \cdot)\)	n/a	19456	64
7803.2.bu	\(\chi_{7803}(80, \cdot)\)	n/a	52224	128
7803.2.bx	\(\chi_{7803}(16, \cdot)\)	n/a	87936	96
7803.2.by	\(\chi_{7803}(19, \cdot)\)	n/a	38912	128
7803.2.ca	\(\chi_{7803}(4, \cdot)\)	n/a	175872	192
7803.2.cd	\(\chi_{7803}(44, \cdot)\)	n/a	77824	256
7803.2.cf	\(\chi_{7803}(25, \cdot)\)	n/a	351744	384
7803.2.cg	\(\chi_{7803}(5, \cdot)\)	n/a	703488	768

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7803))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7803)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(459))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2601))\)\(^{\oplus 2}\)