Space of modular forms of level 9522 and weight 2

• Label: 9522.2
• Level: 9522
• Weight: 2
• Dimension: 660860
• Nonzero newspaces: 16
• Sturm bound: 10055232

Defining parameters

Level:	\( N \)	=	\( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(10055232\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9522))\).

	Total	New	Old
Modular forms	2525776	660860	1864916
Cusp forms	2501841	660860	1840981
Eisenstein series	23935	0	23935

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9522))\)

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
9522.2.a	\(\chi_{9522}(1, \cdot)\)	9522.2.a.a	1	1
		9522.2.a.b	1
		9522.2.a.c	1
		9522.2.a.d	1
		9522.2.a.e	1
		9522.2.a.f	1
		9522.2.a.g	1
		9522.2.a.h	1
		9522.2.a.i	1
		9522.2.a.j	1
		9522.2.a.k	1
		9522.2.a.l	1
		9522.2.a.m	1
		9522.2.a.n	1
		9522.2.a.o	1
		9522.2.a.p	1
		9522.2.a.q	2
		9522.2.a.r	2
		9522.2.a.s	2
		9522.2.a.t	2
		9522.2.a.u	2
		9522.2.a.v	2
		9522.2.a.w	2
		9522.2.a.x	2
		9522.2.a.y	2
		9522.2.a.z	2
		9522.2.a.ba	2
		9522.2.a.bb	2
		9522.2.a.bc	2
		9522.2.a.bd	2
		9522.2.a.be	2
		9522.2.a.bf	2
		9522.2.a.bg	2
		9522.2.a.bh	2
		9522.2.a.bi	2
		9522.2.a.bj	2
		9522.2.a.bk	2
		9522.2.a.bl	4
		9522.2.a.bm	4
		9522.2.a.bn	4
		9522.2.a.bo	4
		9522.2.a.bp	5
		9522.2.a.bq	5
		9522.2.a.br	5
		9522.2.a.bs	5
		9522.2.a.bt	5
		9522.2.a.bu	5
		9522.2.a.bv	5
		9522.2.a.bw	5
		9522.2.a.bx	5
		9522.2.a.by	5
		9522.2.a.bz	5
		9522.2.a.ca	5
		9522.2.a.cb	6
		9522.2.a.cc	6
		9522.2.a.cd	8
		9522.2.a.ce	8
		9522.2.a.cf	8
		9522.2.a.cg	10
		9522.2.a.ch	10
		9522.2.a.ci	10
		9522.2.a.cj	10
9522.2.d	\(\chi_{9522}(9521, \cdot)\)	n/a	168	1
9522.2.e	\(\chi_{9522}(3175, \cdot)\)	n/a	1010	2
9522.2.f	\(\chi_{9522}(3173, \cdot)\)	n/a	1008	2
9522.2.i	\(\chi_{9522}(487, \cdot)\)	n/a	2100	10
9522.2.j	\(\chi_{9522}(359, \cdot)\)	n/a	1680	10
9522.2.m	\(\chi_{9522}(415, \cdot)\)	n/a	5060	22
9522.2.n	\(\chi_{9522}(1705, \cdot)\)	n/a	10080	20
9522.2.o	\(\chi_{9522}(413, \cdot)\)	n/a	4048	22
9522.2.t	\(\chi_{9522}(263, \cdot)\)	n/a	10080	20
9522.2.u	\(\chi_{9522}(139, \cdot)\)	n/a	24288	44
9522.2.x	\(\chi_{9522}(137, \cdot)\)	n/a	24288	44
9522.2.y	\(\chi_{9522}(55, \cdot)\)	n/a	50600	220
9522.2.bb	\(\chi_{9522}(17, \cdot)\)	n/a	40480	220
9522.2.bc	\(\chi_{9522}(13, \cdot)\)	n/a	242880	440
9522.2.bd	\(\chi_{9522}(5, \cdot)\)	n/a	242880	440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9522))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9522)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1587))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4761))\)\(^{\oplus 2}\)