Space of modular forms of level 7225 and weight 2

• Label: 7225.2
• Level: 7225
• Weight: 2
• Dimension: 1897000
• Nonzero newspaces: 40
• Sturm bound: 8323200

Defining parameters

Level:	\( N \)	=	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(8323200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7225))\).

	Total	New	Old
Modular forms	2092000	1912109	179891
Cusp forms	2069601	1897000	172601
Eisenstein series	22399	15109	7290

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7225))\)

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
7225.2.a	\(\chi_{7225}(1, \cdot)\)	7225.2.a.a	1	1
		7225.2.a.b	1
		7225.2.a.c	1
		7225.2.a.d	1
		7225.2.a.e	1
		7225.2.a.f	1
		7225.2.a.g	1
		7225.2.a.h	1
		7225.2.a.i	2
		7225.2.a.j	2
		7225.2.a.k	2
		7225.2.a.l	2
		7225.2.a.m	2
		7225.2.a.n	2
		7225.2.a.o	2
		7225.2.a.p	2
		7225.2.a.q	3
		7225.2.a.r	3
		7225.2.a.s	3
		7225.2.a.t	3
		7225.2.a.u	4
		7225.2.a.v	4
		7225.2.a.w	4
		7225.2.a.x	5
		7225.2.a.y	5
		7225.2.a.z	6
		7225.2.a.ba	6
		7225.2.a.bb	6
		7225.2.a.bc	6
		7225.2.a.bd	6
		7225.2.a.be	6
		7225.2.a.bf	6
		7225.2.a.bg	6
		7225.2.a.bh	6
		7225.2.a.bi	6
		7225.2.a.bj	8
		7225.2.a.bk	8
		7225.2.a.bl	8
		7225.2.a.bm	12
		7225.2.a.bn	12
		7225.2.a.bo	12
		7225.2.a.bp	12
		7225.2.a.bq	12
		7225.2.a.br	12
		7225.2.a.bs	12
		7225.2.a.bt	15
		7225.2.a.bu	15
		7225.2.a.bv	15
		7225.2.a.bw	15
		7225.2.a.bx	24
		7225.2.a.by	24
		7225.2.a.bz	24
		7225.2.a.ca	24
		7225.2.a.cb	24
7225.2.b	\(\chi_{7225}(2024, \cdot)\)	n/a	392	1
7225.2.c	\(\chi_{7225}(7224, \cdot)\)	n/a	392	1
7225.2.d	\(\chi_{7225}(5201, \cdot)\)	n/a	406	1
7225.2.e	\(\chi_{7225}(251, \cdot)\)	n/a	812	2
7225.2.j	\(\chi_{7225}(2274, \cdot)\)	n/a	784	2
7225.2.k	\(\chi_{7225}(1446, \cdot)\)	n/a	2652	4
7225.2.m	\(\chi_{7225}(1001, \cdot)\)	n/a	1628	4
7225.2.n	\(\chi_{7225}(399, \cdot)\)	n/a	1560	4
7225.2.p	\(\chi_{7225}(866, \cdot)\)	n/a	2648	4
7225.2.q	\(\chi_{7225}(1444, \cdot)\)	n/a	2640	4
7225.2.r	\(\chi_{7225}(579, \cdot)\)	n/a	2648	4
7225.2.s	\(\chi_{7225}(643, \cdot)\)	n/a	3128	8
7225.2.v	\(\chi_{7225}(618, \cdot)\)	n/a	3128	8
7225.2.w	\(\chi_{7225}(426, \cdot)\)	n/a	7712	16
7225.2.x	\(\chi_{7225}(829, \cdot)\)	n/a	5280	8
7225.2.bc	\(\chi_{7225}(616, \cdot)\)	n/a	5296	8
7225.2.bd	\(\chi_{7225}(101, \cdot)\)	n/a	7712	16
7225.2.be	\(\chi_{7225}(424, \cdot)\)	n/a	7296	16
7225.2.bf	\(\chi_{7225}(324, \cdot)\)	n/a	7296	16
7225.2.bh	\(\chi_{7225}(134, \cdot)\)	n/a	10592	16
7225.2.bi	\(\chi_{7225}(1046, \cdot)\)	n/a	10560	16
7225.2.bk	\(\chi_{7225}(149, \cdot)\)	n/a	14592	32
7225.2.bp	\(\chi_{7225}(276, \cdot)\)	n/a	15424	32
7225.2.bq	\(\chi_{7225}(447, \cdot)\)	n/a	21152	32
7225.2.bt	\(\chi_{7225}(158, \cdot)\)	n/a	21152	32
7225.2.bu	\(\chi_{7225}(86, \cdot)\)	n/a	48768	64
7225.2.bw	\(\chi_{7225}(49, \cdot)\)	n/a	29312	64
7225.2.bx	\(\chi_{7225}(26, \cdot)\)	n/a	30784	64
7225.2.bz	\(\chi_{7225}(69, \cdot)\)	n/a	48896	64
7225.2.ca	\(\chi_{7225}(84, \cdot)\)	n/a	48896	64
7225.2.cb	\(\chi_{7225}(16, \cdot)\)	n/a	48768	64
7225.2.cc	\(\chi_{7225}(82, \cdot)\)	n/a	58496	128
7225.2.cf	\(\chi_{7225}(7, \cdot)\)	n/a	58496	128
7225.2.cg	\(\chi_{7225}(21, \cdot)\)	n/a	97536	128
7225.2.cl	\(\chi_{7225}(4, \cdot)\)	n/a	97792	128
7225.2.cn	\(\chi_{7225}(36, \cdot)\)	n/a	195584	256
7225.2.co	\(\chi_{7225}(9, \cdot)\)	n/a	195072	256
7225.2.cq	\(\chi_{7225}(3, \cdot)\)	n/a	390656	512
7225.2.ct	\(\chi_{7225}(12, \cdot)\)	n/a	390656	512

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7225))\)\(^{\oplus 1}\)