Space of modular forms of level 5175 and weight 2

• Label: 5175.2
• Level: 5175
• Weight: 2
• Dimension: 686961
• Nonzero newspaces: 48
• Sturm bound: 3801600

Defining parameters

Level:	\( N \)	=	\( 5175 = 3^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(3801600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5175))\).

	Total	New	Old
Modular forms	960256	694709	265547
Cusp forms	940545	686961	253584
Eisenstein series	19711	7748	11963

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5175))\)

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
5175.2.a	\(\chi_{5175}(1, \cdot)\)	5175.2.a.a	1	1
		5175.2.a.b	1
		5175.2.a.c	1
		5175.2.a.d	1
		5175.2.a.e	1
		5175.2.a.f	1
		5175.2.a.g	1
		5175.2.a.h	1
		5175.2.a.i	1
		5175.2.a.j	1
		5175.2.a.k	1
		5175.2.a.l	1
		5175.2.a.m	1
		5175.2.a.n	1
		5175.2.a.o	1
		5175.2.a.p	1
		5175.2.a.q	1
		5175.2.a.r	1
		5175.2.a.s	1
		5175.2.a.t	1
		5175.2.a.u	1
		5175.2.a.v	1
		5175.2.a.w	1
		5175.2.a.x	1
		5175.2.a.y	1
		5175.2.a.z	1
		5175.2.a.ba	2
		5175.2.a.bb	2
		5175.2.a.bc	2
		5175.2.a.bd	2
		5175.2.a.be	2
		5175.2.a.bf	2
		5175.2.a.bg	2
		5175.2.a.bh	2
		5175.2.a.bi	2
		5175.2.a.bj	2
		5175.2.a.bk	2
		5175.2.a.bl	2
		5175.2.a.bm	2
		5175.2.a.bn	2
		5175.2.a.bo	2
		5175.2.a.bp	2
		5175.2.a.bq	3
		5175.2.a.br	3
		5175.2.a.bs	3
		5175.2.a.bt	3
		5175.2.a.bu	3
		5175.2.a.bv	4
		5175.2.a.bw	4
		5175.2.a.bx	4
		5175.2.a.by	6
		5175.2.a.bz	6
		5175.2.a.ca	7
		5175.2.a.cb	7
		5175.2.a.cc	7
		5175.2.a.cd	7
		5175.2.a.ce	7
		5175.2.a.cf	7
		5175.2.a.cg	7
		5175.2.a.ch	7
		5175.2.a.ci	10
		5175.2.a.cj	10
5175.2.b	\(\chi_{5175}(2899, \cdot)\)	n/a	166	1
5175.2.c	\(\chi_{5175}(2276, \cdot)\)	n/a	152	1
5175.2.h	\(\chi_{5175}(5174, \cdot)\)	n/a	144	1
5175.2.i	\(\chi_{5175}(1726, \cdot)\)	n/a	836	2
5175.2.j	\(\chi_{5175}(2393, \cdot)\)	n/a	264	2
5175.2.k	\(\chi_{5175}(2368, \cdot)\)	n/a	356	2
5175.2.n	\(\chi_{5175}(1036, \cdot)\)	n/a	1104	4
5175.2.o	\(\chi_{5175}(1724, \cdot)\)	n/a	856	2
5175.2.t	\(\chi_{5175}(551, \cdot)\)	n/a	900	2
5175.2.u	\(\chi_{5175}(1174, \cdot)\)	n/a	792	2
5175.2.x	\(\chi_{5175}(1034, \cdot)\)	n/a	960	4
5175.2.y	\(\chi_{5175}(206, \cdot)\)	n/a	960	4
5175.2.z	\(\chi_{5175}(829, \cdot)\)	n/a	1096	4
5175.2.bc	\(\chi_{5175}(676, \cdot)\)	n/a	1870	10
5175.2.bf	\(\chi_{5175}(668, \cdot)\)	n/a	1584	4
5175.2.bg	\(\chi_{5175}(643, \cdot)\)	n/a	1712	4
5175.2.bh	\(\chi_{5175}(346, \cdot)\)	n/a	5280	8
5175.2.bk	\(\chi_{5175}(298, \cdot)\)	n/a	2384	8
5175.2.bl	\(\chi_{5175}(323, \cdot)\)	n/a	1760	8
5175.2.bm	\(\chi_{5175}(224, \cdot)\)	n/a	1440	10
5175.2.br	\(\chi_{5175}(251, \cdot)\)	n/a	1520	10
5175.2.bs	\(\chi_{5175}(1099, \cdot)\)	n/a	1780	10
5175.2.bv	\(\chi_{5175}(139, \cdot)\)	n/a	5280	8
5175.2.bw	\(\chi_{5175}(896, \cdot)\)	n/a	5728	8
5175.2.bx	\(\chi_{5175}(344, \cdot)\)	n/a	5728	8
5175.2.ca	\(\chi_{5175}(151, \cdot)\)	n/a	9000	20
5175.2.cd	\(\chi_{5175}(343, \cdot)\)	n/a	3560	20
5175.2.ce	\(\chi_{5175}(593, \cdot)\)	n/a	2880	20
5175.2.cf	\(\chi_{5175}(271, \cdot)\)	n/a	11920	40
5175.2.cg	\(\chi_{5175}(22, \cdot)\)	n/a	11456	16
5175.2.ch	\(\chi_{5175}(47, \cdot)\)	n/a	10560	16
5175.2.ck	\(\chi_{5175}(49, \cdot)\)	n/a	8560	20
5175.2.cl	\(\chi_{5175}(176, \cdot)\)	n/a	9000	20
5175.2.cq	\(\chi_{5175}(74, \cdot)\)	n/a	8560	20
5175.2.ct	\(\chi_{5175}(64, \cdot)\)	n/a	11920	40
5175.2.cu	\(\chi_{5175}(296, \cdot)\)	n/a	9600	40
5175.2.cv	\(\chi_{5175}(44, \cdot)\)	n/a	9600	40
5175.2.cy	\(\chi_{5175}(7, \cdot)\)	n/a	17120	40
5175.2.cz	\(\chi_{5175}(32, \cdot)\)	n/a	17120	40
5175.2.dc	\(\chi_{5175}(16, \cdot)\)	n/a	57280	80
5175.2.dd	\(\chi_{5175}(8, \cdot)\)	n/a	19200	80
5175.2.de	\(\chi_{5175}(28, \cdot)\)	n/a	23840	80
5175.2.dj	\(\chi_{5175}(14, \cdot)\)	n/a	57280	80
5175.2.dk	\(\chi_{5175}(11, \cdot)\)	n/a	57280	80
5175.2.dl	\(\chi_{5175}(4, \cdot)\)	n/a	57280	80
5175.2.dq	\(\chi_{5175}(2, \cdot)\)	n/a	114560	160
5175.2.dr	\(\chi_{5175}(67, \cdot)\)	n/a	114560	160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5175))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5175)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1725))\)\(^{\oplus 2}\)