Space of modular forms of level 8303 and weight 2

• Label: 8303.2
• Level: 8303
• Weight: 2
• Dimension: 2822695
• Nonzero newspaces: 24
• Sturm bound: 11436480

Defining parameters

Level:	\( N \)	=	\( 8303 = 19^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(11436480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8303))\).

	Total	New	Old
Modular forms	2870208	2842371	27837
Cusp forms	2848033	2822695	25338
Eisenstein series	22175	19676	2499

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8303))\)

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
8303.2.a	\(\chi_{8303}(1, \cdot)\)	8303.2.a.a	1	1
		8303.2.a.b	1
		8303.2.a.c	2
		8303.2.a.d	2
		8303.2.a.e	2
		8303.2.a.f	2
		8303.2.a.g	5
		8303.2.a.h	6
		8303.2.a.i	6
		8303.2.a.j	8
		8303.2.a.k	12
		8303.2.a.l	13
		8303.2.a.m	13
		8303.2.a.n	14
		8303.2.a.o	19
		8303.2.a.p	19
		8303.2.a.q	20
		8303.2.a.r	26
		8303.2.a.s	26
		8303.2.a.t	38
		8303.2.a.u	38
		8303.2.a.v	54
		8303.2.a.w	54
		8303.2.a.x	54
		8303.2.a.y	54
		8303.2.a.z	56
		8303.2.a.ba	80
8303.2.b	\(\chi_{8303}(8302, \cdot)\)	n/a	664	1
8303.2.e	\(\chi_{8303}(1151, \cdot)\)	n/a	1244	2
8303.2.h	\(\chi_{8303}(3679, \cdot)\)	n/a	1328	2
8303.2.i	\(\chi_{8303}(415, \cdot)\)	n/a	3744	6
8303.2.j	\(\chi_{8303}(1084, \cdot)\)	n/a	6650	10
8303.2.m	\(\chi_{8303}(2138, \cdot)\)	n/a	3984	6
8303.2.n	\(\chi_{8303}(438, \cdot)\)	n/a	12564	18
8303.2.q	\(\chi_{8303}(360, \cdot)\)	n/a	6640	10
8303.2.r	\(\chi_{8303}(292, \cdot)\)	n/a	13280	20
8303.2.u	\(\chi_{8303}(436, \cdot)\)	n/a	13644	18
8303.2.v	\(\chi_{8303}(254, \cdot)\)	n/a	25128	36
8303.2.w	\(\chi_{8303}(293, \cdot)\)	n/a	13280	20
8303.2.z	\(\chi_{8303}(54, \cdot)\)	n/a	39840	60
8303.2.ba	\(\chi_{8303}(160, \cdot)\)	n/a	27288	36
8303.2.bd	\(\chi_{8303}(24, \cdot)\)	n/a	75168	108
8303.2.be	\(\chi_{8303}(333, \cdot)\)	n/a	39840	60
8303.2.bh	\(\chi_{8303}(39, \cdot)\)	n/a	136440	180
8303.2.bi	\(\chi_{8303}(22, \cdot)\)	n/a	81864	108
8303.2.bl	\(\chi_{8303}(37, \cdot)\)	n/a	136440	180
8303.2.bo	\(\chi_{8303}(26, \cdot)\)	n/a	272880	360
8303.2.br	\(\chi_{8303}(65, \cdot)\)	n/a	272880	360
8303.2.bs	\(\chi_{8303}(4, \cdot)\)	n/a	818640	1080
8303.2.bv	\(\chi_{8303}(10, \cdot)\)	n/a	818640	1080

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8303))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8303)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(437))\)\(^{\oplus 2}\)