Space of modular forms of level 7569 and weight 2

• Label: 7569.2
• Level: 7569
• Weight: 2
• Dimension: 1668639
• Nonzero newspaces: 24
• Sturm bound: 8477280

Defining parameters

Level:	\( N \)	=	\( 7569 = 3^{2} \cdot 29^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(8477280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7569))\).

	Total	New	Old
Modular forms	2128952	1678976	449976
Cusp forms	2109689	1668639	441050
Eisenstein series	19263	10337	8926

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7569))\)

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
7569.2.a	\(\chi_{7569}(1, \cdot)\)	7569.2.a.a	1	1
		7569.2.a.b	1
		7569.2.a.c	2
		7569.2.a.d	2
		7569.2.a.e	2
		7569.2.a.f	2
		7569.2.a.g	2
		7569.2.a.h	2
		7569.2.a.i	2
		7569.2.a.j	2
		7569.2.a.k	2
		7569.2.a.l	2
		7569.2.a.m	2
		7569.2.a.n	2
		7569.2.a.o	2
		7569.2.a.p	3
		7569.2.a.q	3
		7569.2.a.r	3
		7569.2.a.s	3
		7569.2.a.t	3
		7569.2.a.u	4
		7569.2.a.v	4
		7569.2.a.w	4
		7569.2.a.x	4
		7569.2.a.y	6
		7569.2.a.z	6
		7569.2.a.ba	6
		7569.2.a.bb	6
		7569.2.a.bc	6
		7569.2.a.bd	8
		7569.2.a.be	8
		7569.2.a.bf	8
		7569.2.a.bg	8
		7569.2.a.bh	8
		7569.2.a.bi	8
		7569.2.a.bj	9
		7569.2.a.bk	9
		7569.2.a.bl	9
		7569.2.a.bm	9
		7569.2.a.bn	12
		7569.2.a.bo	12
		7569.2.a.bp	12
		7569.2.a.bq	12
		7569.2.a.br	12
		7569.2.a.bs	12
		7569.2.a.bt	12
		7569.2.a.bu	16
		7569.2.a.bv	16
		7569.2.a.bw	36
7569.2.c	\(\chi_{7569}(4204, \cdot)\)	n/a	324	1
7569.2.e	\(\chi_{7569}(2524, \cdot)\)	n/a	1568	2
7569.2.g	\(\chi_{7569}(800, \cdot)\)	n/a	540	2
7569.2.i	\(\chi_{7569}(1681, \cdot)\)	n/a	1568	2
7569.2.k	\(\chi_{7569}(190, \cdot)\)	n/a	1950	6
7569.2.l	\(\chi_{7569}(41, \cdot)\)	n/a	3136	4
7569.2.o	\(\chi_{7569}(1108, \cdot)\)	n/a	1944	6
7569.2.q	\(\chi_{7569}(571, \cdot)\)	n/a	9408	12
7569.2.r	\(\chi_{7569}(467, \cdot)\)	n/a	3240	12
7569.2.t	\(\chi_{7569}(262, \cdot)\)	n/a	10108	28
7569.2.v	\(\chi_{7569}(196, \cdot)\)	n/a	9408	12
7569.2.y	\(\chi_{7569}(28, \cdot)\)	n/a	10136	28
7569.2.bb	\(\chi_{7569}(14, \cdot)\)	n/a	18816	24
7569.2.bc	\(\chi_{7569}(88, \cdot)\)	n/a	48608	56
7569.2.bd	\(\chi_{7569}(17, \cdot)\)	n/a	16240	56
7569.2.bg	\(\chi_{7569}(115, \cdot)\)	n/a	48608	56
7569.2.bi	\(\chi_{7569}(82, \cdot)\)	n/a	60648	168
7569.2.bk	\(\chi_{7569}(104, \cdot)\)	n/a	97216	112
7569.2.bm	\(\chi_{7569}(64, \cdot)\)	n/a	60816	168
7569.2.bo	\(\chi_{7569}(7, \cdot)\)	n/a	291648	336
7569.2.bq	\(\chi_{7569}(8, \cdot)\)	n/a	97440	336
7569.2.bs	\(\chi_{7569}(4, \cdot)\)	n/a	291648	336
7569.2.bu	\(\chi_{7569}(2, \cdot)\)	n/a	583296	672

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7569))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7569)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2523))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7569))\)\(^{\oplus 1}\)