Space of modular forms of level 9386 and weight 2

• Label: 9386.2
• Level: 9386
• Weight: 2
• Dimension: 893915
• Nonzero newspaces: 48
• Sturm bound: 10916640

Defining parameters

Level:	\( N \)	=	\( 9386 = 2 \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(10916640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9386))\).

	Total	New	Old
Modular forms	2741256	893915	1847341
Cusp forms	2717065	893915	1823150
Eisenstein series	24191	0	24191

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9386))\)

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
9386.2.a	\(\chi_{9386}(1, \cdot)\)	9386.2.a.a	1	1
		9386.2.a.b	1
		9386.2.a.c	1
		9386.2.a.d	1
		9386.2.a.e	1
		9386.2.a.f	1
		9386.2.a.g	1
		9386.2.a.h	1
		9386.2.a.i	1
		9386.2.a.j	1
		9386.2.a.k	1
		9386.2.a.l	1
		9386.2.a.m	1
		9386.2.a.n	1
		9386.2.a.o	2
		9386.2.a.p	2
		9386.2.a.q	2
		9386.2.a.r	2
		9386.2.a.s	2
		9386.2.a.t	2
		9386.2.a.u	3
		9386.2.a.v	3
		9386.2.a.w	3
		9386.2.a.x	3
		9386.2.a.y	3
		9386.2.a.z	3
		9386.2.a.ba	3
		9386.2.a.bb	3
		9386.2.a.bc	3
		9386.2.a.bd	3
		9386.2.a.be	3
		9386.2.a.bf	4
		9386.2.a.bg	4
		9386.2.a.bh	4
		9386.2.a.bi	6
		9386.2.a.bj	6
		9386.2.a.bk	6
		9386.2.a.bl	6
		9386.2.a.bm	6
		9386.2.a.bn	6
		9386.2.a.bo	9
		9386.2.a.bp	9
		9386.2.a.bq	12
		9386.2.a.br	12
		9386.2.a.bs	12
		9386.2.a.bt	12
		9386.2.a.bu	12
		9386.2.a.bv	12
		9386.2.a.bw	15
		9386.2.a.bx	15
		9386.2.a.by	15
		9386.2.a.bz	15
		9386.2.a.ca	18
		9386.2.a.cb	18
		9386.2.a.cc	24
		9386.2.a.cd	24
9386.2.d	\(\chi_{9386}(6499, \cdot)\)	n/a	396	1
9386.2.e	\(\chi_{9386}(653, \cdot)\)	n/a	796	2
9386.2.f	\(\chi_{9386}(1873, \cdot)\)	n/a	680	2
9386.2.g	\(\chi_{9386}(2167, \cdot)\)	n/a	798	2
9386.2.h	\(\chi_{9386}(4761, \cdot)\)	n/a	796	2
9386.2.i	\(\chi_{9386}(3609, \cdot)\)	n/a	788	2
9386.2.m	\(\chi_{9386}(3611, \cdot)\)	n/a	796	2
9386.2.n	\(\chi_{9386}(4263, \cdot)\)	n/a	788	2
9386.2.o	\(\chi_{9386}(1375, \cdot)\)	n/a	796	2
9386.2.v	\(\chi_{9386}(2097, \cdot)\)	n/a	796	2
9386.2.w	\(\chi_{9386}(2265, \cdot)\)	n/a	2376	6
9386.2.x	\(\chi_{9386}(1145, \cdot)\)	n/a	2040	6
9386.2.y	\(\chi_{9386}(1543, \cdot)\)	n/a	2376	6
9386.2.z	\(\chi_{9386}(2459, \cdot)\)	n/a	1592	4
9386.2.bd	\(\chi_{9386}(293, \cdot)\)	n/a	1592	4
9386.2.be	\(\chi_{9386}(721, \cdot)\)	n/a	1592	4
9386.2.bf	\(\chi_{9386}(1513, \cdot)\)	n/a	1576	4
9386.2.bh	\(\chi_{9386}(1317, \cdot)\)	n/a	2376	6
9386.2.bl	\(\chi_{9386}(389, \cdot)\)	n/a	2388	6
9386.2.bm	\(\chi_{9386}(595, \cdot)\)	n/a	2376	6
9386.2.bq	\(\chi_{9386}(495, \cdot)\)	n/a	6840	18
9386.2.bu	\(\chi_{9386}(1029, \cdot)\)	n/a	4752	12
9386.2.bv	\(\chi_{9386}(1021, \cdot)\)	n/a	4752	12
9386.2.bw	\(\chi_{9386}(307, \cdot)\)	n/a	4776	12
9386.2.bx	\(\chi_{9386}(77, \cdot)\)	n/a	8028	18
9386.2.ca	\(\chi_{9386}(315, \cdot)\)	n/a	15912	36
9386.2.cb	\(\chi_{9386}(191, \cdot)\)	n/a	15912	36
9386.2.cc	\(\chi_{9386}(235, \cdot)\)	n/a	13680	36
9386.2.cd	\(\chi_{9386}(87, \cdot)\)	n/a	15912	36
9386.2.cf	\(\chi_{9386}(151, \cdot)\)	n/a	16056	36
9386.2.cg	\(\chi_{9386}(49, \cdot)\)	n/a	15912	36
9386.2.cn	\(\chi_{9386}(277, \cdot)\)	n/a	15912	36
9386.2.co	\(\chi_{9386}(311, \cdot)\)	n/a	16056	36
9386.2.cp	\(\chi_{9386}(153, \cdot)\)	n/a	15912	36
9386.2.cs	\(\chi_{9386}(9, \cdot)\)	n/a	47952	108
9386.2.ct	\(\chi_{9386}(131, \cdot)\)	n/a	41040	108
9386.2.cu	\(\chi_{9386}(35, \cdot)\)	n/a	47952	108
9386.2.cw	\(\chi_{9386}(31, \cdot)\)	n/a	32112	72
9386.2.cx	\(\chi_{9386}(37, \cdot)\)	n/a	31824	72
9386.2.cy	\(\chi_{9386}(145, \cdot)\)	n/a	31824	72
9386.2.dc	\(\chi_{9386}(141, \cdot)\)	n/a	31824	72
9386.2.dg	\(\chi_{9386}(17, \cdot)\)	n/a	47952	108
9386.2.dh	\(\chi_{9386}(25, \cdot)\)	n/a	47736	108
9386.2.dl	\(\chi_{9386}(199, \cdot)\)	n/a	47952	108
9386.2.dm	\(\chi_{9386}(21, \cdot)\)	n/a	95472	216
9386.2.dn	\(\chi_{9386}(15, \cdot)\)	n/a	95904	216
9386.2.do	\(\chi_{9386}(41, \cdot)\)	n/a	95904	216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9386))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9386)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(494))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4693))\)\(^{\oplus 2}\)