Space of modular forms of level 9025 and weight 2

• Label: 9025.2
• Level: 9025
• Weight: 2
• Dimension: 2968323
• Nonzero newspaces: 36
• Sturm bound: 12996000

Defining parameters

Level:	\( N \)	=	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(12996000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9025))\).

	Total	New	Old
Modular forms	3263112	2987532	275580
Cusp forms	3234889	2968323	266566
Eisenstein series	28223	19209	9014

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9025))\)

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
9025.2.a	\(\chi_{9025}(1, \cdot)\)	9025.2.a.a	1	1
		9025.2.a.b	1
		9025.2.a.c	1
		9025.2.a.d	1
		9025.2.a.e	1
		9025.2.a.f	1
		9025.2.a.g	1
		9025.2.a.h	1
		9025.2.a.i	1
		9025.2.a.j	1
		9025.2.a.k	2
		9025.2.a.l	2
		9025.2.a.m	2
		9025.2.a.n	2
		9025.2.a.o	2
		9025.2.a.p	2
		9025.2.a.q	2
		9025.2.a.r	2
		9025.2.a.s	2
		9025.2.a.t	2
		9025.2.a.u	2
		9025.2.a.v	2
		9025.2.a.w	3
		9025.2.a.x	3
		9025.2.a.y	3
		9025.2.a.z	3
		9025.2.a.ba	3
		9025.2.a.bb	3
		9025.2.a.bc	3
		9025.2.a.bd	3
		9025.2.a.be	3
		9025.2.a.bf	4
		9025.2.a.bg	4
		9025.2.a.bh	4
		9025.2.a.bi	4
		9025.2.a.bj	4
		9025.2.a.bk	4
		9025.2.a.bl	4
		9025.2.a.bm	4
		9025.2.a.bn	4
		9025.2.a.bo	4
		9025.2.a.bp	4
		9025.2.a.bq	6
		9025.2.a.br	6
		9025.2.a.bs	6
		9025.2.a.bt	6
		9025.2.a.bu	6
		9025.2.a.bv	6
		9025.2.a.bw	6
		9025.2.a.bx	6
		9025.2.a.by	6
		9025.2.a.bz	6
		9025.2.a.ca	6
		9025.2.a.cb	8
		9025.2.a.cc	9
		9025.2.a.cd	9
		9025.2.a.ce	9
		9025.2.a.cf	9
		9025.2.a.cg	10
		9025.2.a.ch	10
		9025.2.a.ci	10
		9025.2.a.cj	10
		9025.2.a.ck	16
		9025.2.a.cl	16
9025.2.a.cm	16
9025.2.a.cn	20
9025.2.a.co	20
9025.2.a.cp	21
9025.2.a.cq	21
9025.2.a.cr	21
9025.2.a.cs	21
9025.2.a.ct	24
9025.2.a.cu	24
9025.2.a.cv	40
9025.2.b	\(\chi_{9025}(6499, \cdot)\)	n/a	494	1
9025.2.e	\(\chi_{9025}(1151, \cdot)\)	n/a	1030	2
9025.2.g	\(\chi_{9025}(1082, \cdot)\)	n/a	988	2
9025.2.h	\(\chi_{9025}(1806, \cdot)\)	n/a	3340	4
9025.2.j	\(\chi_{9025}(4624, \cdot)\)	n/a	988	2
9025.2.l	\(\chi_{9025}(776, \cdot)\)	n/a	3084	6
9025.2.n	\(\chi_{9025}(1084, \cdot)\)	n/a	3344	4
9025.2.p	\(\chi_{9025}(293, \cdot)\)	n/a	1976	4
9025.2.r	\(\chi_{9025}(1736, \cdot)\)	n/a	6672	8
9025.2.u	\(\chi_{9025}(99, \cdot)\)	n/a	2964	6
9025.2.v	\(\chi_{9025}(476, \cdot)\)	n/a	10764	18
9025.2.w	\(\chi_{9025}(2887, \cdot)\)	n/a	6672	8
9025.2.y	\(\chi_{9025}(429, \cdot)\)	n/a	6672	8
9025.2.bc	\(\chi_{9025}(307, \cdot)\)	n/a	5928	12
9025.2.bf	\(\chi_{9025}(324, \cdot)\)	n/a	10224	18
9025.2.bg	\(\chi_{9025}(606, \cdot)\)	n/a	20016	24
9025.2.bh	\(\chi_{9025}(26, \cdot)\)	n/a	21528	36
9025.2.bj	\(\chi_{9025}(1152, \cdot)\)	n/a	13344	16
9025.2.bk	\(\chi_{9025}(18, \cdot)\)	n/a	20448	36
9025.2.bn	\(\chi_{9025}(54, \cdot)\)	n/a	20016	24
9025.2.bp	\(\chi_{9025}(96, \cdot)\)	n/a	68256	72
9025.2.br	\(\chi_{9025}(49, \cdot)\)	n/a	20448	36
9025.2.bt	\(\chi_{9025}(101, \cdot)\)	n/a	64692	108
9025.2.bu	\(\chi_{9025}(127, \cdot)\)	n/a	40032	48
9025.2.bx	\(\chi_{9025}(39, \cdot)\)	n/a	68256	72
9025.2.ca	\(\chi_{9025}(107, \cdot)\)	n/a	40896	72
9025.2.cb	\(\chi_{9025}(11, \cdot)\)	n/a	136512	144
9025.2.cc	\(\chi_{9025}(24, \cdot)\)	n/a	61344	108
9025.2.cg	\(\chi_{9025}(37, \cdot)\)	n/a	136512	144
9025.2.cj	\(\chi_{9025}(64, \cdot)\)	n/a	136512	144
9025.2.ck	\(\chi_{9025}(32, \cdot)\)	n/a	122688	216
9025.2.cm	\(\chi_{9025}(6, \cdot)\)	n/a	409536	432
9025.2.cn	\(\chi_{9025}(8, \cdot)\)	n/a	273024	288
9025.2.cq	\(\chi_{9025}(4, \cdot)\)	n/a	409536	432
9025.2.ct	\(\chi_{9025}(2, \cdot)\)	n/a	819072	864

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1805))\)\(^{\oplus 2}\)