Space of modular forms of level 4335 and weight 2

• Label: 4335.2
• Level: 4335
• Weight: 2
• Dimension: 452400
• Nonzero newspaces: 36
• Sturm bound: 2663424

Defining parameters

Level:	\( N \)	=	\( 4335 = 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(2663424\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4335))\).

	Total	New	Old
Modular forms	672256	456824	215432
Cusp forms	659457	452400	207057
Eisenstein series	12799	4424	8375

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4335))\)

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
4335.2.a	\(\chi_{4335}(1, \cdot)\)	4335.2.a.a	1	1
		4335.2.a.b	1
		4335.2.a.c	1
		4335.2.a.d	1
		4335.2.a.e	1
		4335.2.a.f	1
		4335.2.a.g	1
		4335.2.a.h	2
		4335.2.a.i	2
		4335.2.a.j	2
		4335.2.a.k	2
		4335.2.a.l	2
		4335.2.a.m	2
		4335.2.a.n	3
		4335.2.a.o	3
		4335.2.a.p	3
		4335.2.a.q	3
		4335.2.a.r	3
		4335.2.a.s	3
		4335.2.a.t	3
		4335.2.a.u	4
		4335.2.a.v	4
		4335.2.a.w	4
		4335.2.a.x	4
		4335.2.a.y	4
		4335.2.a.z	4
		4335.2.a.ba	4
		4335.2.a.bb	6
		4335.2.a.bc	6
		4335.2.a.bd	8
		4335.2.a.be	8
		4335.2.a.bf	8
		4335.2.a.bg	8
		4335.2.a.bh	9
		4335.2.a.bi	9
		4335.2.a.bj	9
		4335.2.a.bk	9
		4335.2.a.bl	16
		4335.2.a.bm	16
4335.2.b	\(\chi_{4335}(3469, \cdot)\)	n/a	272	1
4335.2.d	\(\chi_{4335}(1444, \cdot)\)	n/a	272	1
4335.2.g	\(\chi_{4335}(2311, \cdot)\)	n/a	180	1
4335.2.j	\(\chi_{4335}(616, \cdot)\)	n/a	360	2
4335.2.k	\(\chi_{4335}(1118, \cdot)\)	n/a	1024	2
4335.2.m	\(\chi_{4335}(1157, \cdot)\)	n/a	1024	2
4335.2.o	\(\chi_{4335}(1733, \cdot)\)	n/a	1024	2
4335.2.r	\(\chi_{4335}(38, \cdot)\)	n/a	1024	2
4335.2.s	\(\chi_{4335}(829, \cdot)\)	n/a	544	2
4335.2.v	\(\chi_{4335}(977, \cdot)\)	n/a	2048	4
4335.2.w	\(\chi_{4335}(2446, \cdot)\)	n/a	720	4
4335.2.z	\(\chi_{4335}(1579, \cdot)\)	n/a	1072	4
4335.2.ba	\(\chi_{4335}(1022, \cdot)\)	n/a	2048	4
4335.2.bd	\(\chi_{4335}(643, \cdot)\)	n/a	2160	8
4335.2.be	\(\chi_{4335}(224, \cdot)\)	n/a	4096	8
4335.2.bg	\(\chi_{4335}(131, \cdot)\)	n/a	2880	8
4335.2.bi	\(\chi_{4335}(538, \cdot)\)	n/a	2160	8
4335.2.bk	\(\chi_{4335}(256, \cdot)\)	n/a	3264	16
4335.2.bm	\(\chi_{4335}(16, \cdot)\)	n/a	3264	16
4335.2.bp	\(\chi_{4335}(169, \cdot)\)	n/a	4864	16
4335.2.br	\(\chi_{4335}(154, \cdot)\)	n/a	4864	16
4335.2.bt	\(\chi_{4335}(4, \cdot)\)	n/a	9728	32
4335.2.bu	\(\chi_{4335}(47, \cdot)\)	n/a	19456	32
4335.2.bx	\(\chi_{4335}(152, \cdot)\)	n/a	19456	32
4335.2.bz	\(\chi_{4335}(137, \cdot)\)	n/a	19456	32
4335.2.cb	\(\chi_{4335}(98, \cdot)\)	n/a	19456	32
4335.2.cc	\(\chi_{4335}(106, \cdot)\)	n/a	6528	32
4335.2.cf	\(\chi_{4335}(2, \cdot)\)	n/a	38912	64
4335.2.ch	\(\chi_{4335}(19, \cdot)\)	n/a	19712	64
4335.2.ci	\(\chi_{4335}(76, \cdot)\)	n/a	13056	64
4335.2.ck	\(\chi_{4335}(53, \cdot)\)	n/a	38912	64
4335.2.cm	\(\chi_{4335}(22, \cdot)\)	n/a	39168	128
4335.2.cp	\(\chi_{4335}(11, \cdot)\)	n/a	52224	128
4335.2.cr	\(\chi_{4335}(14, \cdot)\)	n/a	77824	128
4335.2.ct	\(\chi_{4335}(7, \cdot)\)	n/a	39168	128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4335))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4335)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 2}\)