Space of modular forms of level 4563 and weight 2

• Label: 4563.2
• Level: 4563
• Weight: 2
• Dimension: 595277
• Nonzero newspaces: 48
• Sturm bound: 3066336

Defining parameters

Level:	\( N \)	=	\( 4563 = 3^{3} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(3066336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4563))\).

	Total	New	Old
Modular forms	773424	601821	171603
Cusp forms	759745	595277	164468
Eisenstein series	13679	6544	7135

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4563))\)

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
4563.2.a	\(\chi_{4563}(1, \cdot)\)	4563.2.a.a	1	1
		4563.2.a.b	1
		4563.2.a.c	1
		4563.2.a.d	1
		4563.2.a.e	1
		4563.2.a.f	1
		4563.2.a.g	1
		4563.2.a.h	2
		4563.2.a.i	2
		4563.2.a.j	2
		4563.2.a.k	2
		4563.2.a.l	2
		4563.2.a.m	2
		4563.2.a.n	2
		4563.2.a.o	2
		4563.2.a.p	2
		4563.2.a.q	2
		4563.2.a.r	3
		4563.2.a.s	3
		4563.2.a.t	3
		4563.2.a.u	3
		4563.2.a.v	4
		4563.2.a.w	4
		4563.2.a.x	4
		4563.2.a.y	4
		4563.2.a.z	4
		4563.2.a.ba	4
		4563.2.a.bb	4
		4563.2.a.bc	5
		4563.2.a.bd	5
		4563.2.a.be	5
		4563.2.a.bf	5
		4563.2.a.bg	6
		4563.2.a.bh	6
		4563.2.a.bi	6
		4563.2.a.bj	6
		4563.2.a.bk	8
		4563.2.a.bl	8
		4563.2.a.bm	8
		4563.2.a.bn	12
		4563.2.a.bo	12
		4563.2.a.bp	12
		4563.2.a.bq	12
		4563.2.a.br	12
		4563.2.a.bs	12
4563.2.b	\(\chi_{4563}(1351, \cdot)\)	n/a	206	1
4563.2.e	\(\chi_{4563}(1522, \cdot)\)	n/a	288	2
4563.2.f	\(\chi_{4563}(2557, \cdot)\)	n/a	288	2
4563.2.g	\(\chi_{4563}(2512, \cdot)\)	n/a	410	2
4563.2.h	\(\chi_{4563}(991, \cdot)\)	n/a	288	2
4563.2.i	\(\chi_{4563}(944, \cdot)\)	n/a	412	2
4563.2.l	\(\chi_{4563}(1882, \cdot)\)	n/a	288	2
4563.2.q	\(\chi_{4563}(1837, \cdot)\)	n/a	410	2
4563.2.r	\(\chi_{4563}(316, \cdot)\)	n/a	288	2
4563.2.t	\(\chi_{4563}(2872, \cdot)\)	n/a	288	2
4563.2.w	\(\chi_{4563}(508, \cdot)\)	n/a	2724	6
4563.2.x	\(\chi_{4563}(22, \cdot)\)	n/a	2712	6
4563.2.y	\(\chi_{4563}(529, \cdot)\)	n/a	2712	6
4563.2.ba	\(\chi_{4563}(89, \cdot)\)	n/a	576	4
4563.2.bc	\(\chi_{4563}(746, \cdot)\)	n/a	576	4
4563.2.bd	\(\chi_{4563}(80, \cdot)\)	n/a	820	4
4563.2.bf	\(\chi_{4563}(1610, \cdot)\)	n/a	576	4
4563.2.bh	\(\chi_{4563}(352, \cdot)\)	n/a	2904	12
4563.2.bm	\(\chi_{4563}(337, \cdot)\)	n/a	2712	6
4563.2.bo	\(\chi_{4563}(823, \cdot)\)	n/a	2712	6
4563.2.bp	\(\chi_{4563}(868, \cdot)\)	n/a	2712	6
4563.2.bt	\(\chi_{4563}(298, \cdot)\)	n/a	2904	12
4563.2.bu	\(\chi_{4563}(488, \cdot)\)	n/a	5424	12
4563.2.bx	\(\chi_{4563}(239, \cdot)\)	n/a	5424	12
4563.2.bz	\(\chi_{4563}(587, \cdot)\)	n/a	5424	12
4563.2.ca	\(\chi_{4563}(289, \cdot)\)	n/a	4320	24
4563.2.cb	\(\chi_{4563}(55, \cdot)\)	n/a	5832	24
4563.2.cc	\(\chi_{4563}(100, \cdot)\)	n/a	4320	24
4563.2.cd	\(\chi_{4563}(118, \cdot)\)	n/a	4320	24
4563.2.cf	\(\chi_{4563}(161, \cdot)\)	n/a	5808	24
4563.2.ci	\(\chi_{4563}(64, \cdot)\)	n/a	4320	24
4563.2.ck	\(\chi_{4563}(10, \cdot)\)	n/a	4320	24
4563.2.cl	\(\chi_{4563}(82, \cdot)\)	n/a	5832	24
4563.2.cq	\(\chi_{4563}(127, \cdot)\)	n/a	4320	24
4563.2.cs	\(\chi_{4563}(61, \cdot)\)	n/a	39168	72
4563.2.ct	\(\chi_{4563}(16, \cdot)\)	n/a	39168	72
4563.2.cu	\(\chi_{4563}(40, \cdot)\)	n/a	39168	72
4563.2.cw	\(\chi_{4563}(206, \cdot)\)	n/a	8640	48
4563.2.cy	\(\chi_{4563}(215, \cdot)\)	n/a	11664	48
4563.2.cz	\(\chi_{4563}(8, \cdot)\)	n/a	8640	48
4563.2.db	\(\chi_{4563}(71, \cdot)\)	n/a	8640	48
4563.2.de	\(\chi_{4563}(43, \cdot)\)	n/a	39168	72
4563.2.df	\(\chi_{4563}(4, \cdot)\)	n/a	39168	72
4563.2.dh	\(\chi_{4563}(25, \cdot)\)	n/a	39168	72
4563.2.dm	\(\chi_{4563}(2, \cdot)\)	n/a	78336	144
4563.2.do	\(\chi_{4563}(5, \cdot)\)	n/a	78336	144
4563.2.dr	\(\chi_{4563}(20, \cdot)\)	n/a	78336	144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4563))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4563)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1521))\)\(^{\oplus 2}\)