Space of modular forms of level 5054 and weight 2

• Label: 5054.2
• Level: 5054
• Weight: 2
• Dimension: 247710
• Nonzero newspaces: 32
• Sturm bound: 3119040

Defining parameters

Level:	\( N \)	=	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(3119040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5054))\).

	Total	New	Old
Modular forms	785808	247710	538098
Cusp forms	773713	247710	526003
Eisenstein series	12095	0	12095

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5054))\)

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
5054.2.a	\(\chi_{5054}(1, \cdot)\)	5054.2.a.a	1	1
		5054.2.a.b	1
		5054.2.a.c	1
		5054.2.a.d	2
		5054.2.a.e	2
		5054.2.a.f	2
		5054.2.a.g	2
		5054.2.a.h	2
		5054.2.a.i	2
		5054.2.a.j	2
		5054.2.a.k	2
		5054.2.a.l	2
		5054.2.a.m	2
		5054.2.a.n	2
		5054.2.a.o	2
		5054.2.a.p	2
		5054.2.a.q	3
		5054.2.a.r	3
		5054.2.a.s	3
		5054.2.a.t	3
		5054.2.a.u	3
		5054.2.a.v	4
		5054.2.a.w	4
		5054.2.a.x	4
		5054.2.a.y	4
		5054.2.a.z	6
		5054.2.a.ba	6
		5054.2.a.bb	6
		5054.2.a.bc	6
		5054.2.a.bd	6
		5054.2.a.be	6
		5054.2.a.bf	8
		5054.2.a.bg	8
		5054.2.a.bh	8
		5054.2.a.bi	8
		5054.2.a.bj	9
		5054.2.a.bk	9
		5054.2.a.bl	12
		5054.2.a.bm	12
5054.2.d	\(\chi_{5054}(5053, \cdot)\)	n/a	224	1
5054.2.e	\(\chi_{5054}(723, \cdot)\)	n/a	456	2
5054.2.f	\(\chi_{5054}(4761, \cdot)\)	n/a	340	2
5054.2.g	\(\chi_{5054}(653, \cdot)\)	n/a	456	2
5054.2.h	\(\chi_{5054}(429, \cdot)\)	n/a	456	2
5054.2.k	\(\chi_{5054}(3181, \cdot)\)	n/a	456	2
5054.2.l	\(\chi_{5054}(2887, \cdot)\)	n/a	456	2
5054.2.m	\(\chi_{5054}(69, \cdot)\)	n/a	448	2
5054.2.t	\(\chi_{5054}(2957, \cdot)\)	n/a	456	2
5054.2.u	\(\chi_{5054}(99, \cdot)\)	n/a	1020	6
5054.2.v	\(\chi_{5054}(821, \cdot)\)	n/a	1356	6
5054.2.w	\(\chi_{5054}(389, \cdot)\)	n/a	1356	6
5054.2.x	\(\chi_{5054}(307, \cdot)\)	n/a	1368	6
5054.2.y	\(\chi_{5054}(1055, \cdot)\)	n/a	1356	6
5054.2.bd	\(\chi_{5054}(299, \cdot)\)	n/a	1356	6
5054.2.bg	\(\chi_{5054}(267, \cdot)\)	n/a	3420	18
5054.2.bh	\(\chi_{5054}(265, \cdot)\)	n/a	4608	18
5054.2.bk	\(\chi_{5054}(163, \cdot)\)	n/a	9072	36
5054.2.bl	\(\chi_{5054}(11, \cdot)\)	n/a	9072	36
5054.2.bm	\(\chi_{5054}(197, \cdot)\)	n/a	6840	36
5054.2.bn	\(\chi_{5054}(39, \cdot)\)	n/a	9072	36
5054.2.bo	\(\chi_{5054}(31, \cdot)\)	n/a	9072	36
5054.2.bv	\(\chi_{5054}(27, \cdot)\)	n/a	9216	36
5054.2.bw	\(\chi_{5054}(75, \cdot)\)	n/a	9072	36
5054.2.bx	\(\chi_{5054}(145, \cdot)\)	n/a	9072	36
5054.2.ca	\(\chi_{5054}(25, \cdot)\)	n/a	27432	108
5054.2.cb	\(\chi_{5054}(9, \cdot)\)	n/a	27432	108
5054.2.cc	\(\chi_{5054}(43, \cdot)\)	n/a	20520	108
5054.2.cf	\(\chi_{5054}(33, \cdot)\)	n/a	27432	108
5054.2.ck	\(\chi_{5054}(3, \cdot)\)	n/a	27432	108
5054.2.cl	\(\chi_{5054}(13, \cdot)\)	n/a	27216	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5054))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5054)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2527))\)\(^{\oplus 2}\)