Space of modular forms of level 9610 and weight 2

• Label: 9610.2
• Level: 9610
• Weight: 2
• Dimension: 843919
• Nonzero newspaces: 24
• Sturm bound: 11070720

Defining parameters

Level:	\( N \)	=	\( 9610 = 2 \cdot 5 \cdot 31^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(11070720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9610))\).

	Total	New	Old
Modular forms	2778720	843919	1934801
Cusp forms	2756641	843919	1912722
Eisenstein series	22079	0	22079

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9610))\)

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
9610.2.a	\(\chi_{9610}(1, \cdot)\)	9610.2.a.a	1	1
		9610.2.a.b	1
		9610.2.a.c	2
		9610.2.a.d	2
		9610.2.a.e	2
		9610.2.a.f	2
		9610.2.a.g	2
		9610.2.a.h	2
		9610.2.a.i	2
		9610.2.a.j	2
		9610.2.a.k	2
		9610.2.a.l	2
		9610.2.a.m	2
		9610.2.a.n	2
		9610.2.a.o	2
		9610.2.a.p	2
		9610.2.a.q	3
		9610.2.a.r	3
		9610.2.a.s	3
		9610.2.a.t	3
		9610.2.a.u	3
		9610.2.a.v	3
		9610.2.a.w	3
		9610.2.a.x	3
		9610.2.a.y	3
		9610.2.a.z	4
		9610.2.a.ba	4
		9610.2.a.bb	4
		9610.2.a.bc	4
		9610.2.a.bd	4
		9610.2.a.be	4
		9610.2.a.bf	4
		9610.2.a.bg	4
		9610.2.a.bh	4
		9610.2.a.bi	4
		9610.2.a.bj	4
		9610.2.a.bk	4
		9610.2.a.bl	4
		9610.2.a.bm	4
		9610.2.a.bn	4
		9610.2.a.bo	4
		9610.2.a.bp	4
		9610.2.a.bq	4
		9610.2.a.br	4
		9610.2.a.bs	4
		9610.2.a.bt	4
		9610.2.a.bu	4
		9610.2.a.bv	4
		9610.2.a.bw	4
		9610.2.a.bx	4
		9610.2.a.by	4
		9610.2.a.bz	6
		9610.2.a.ca	8
		9610.2.a.cb	8
		9610.2.a.cc	8
		9610.2.a.cd	8
		9610.2.a.ce	12
		9610.2.a.cf	12
		9610.2.a.cg	12
		9610.2.a.ch	12
		9610.2.a.ci	16
		9610.2.a.cj	24
		9610.2.a.ck	24
9610.2.b	\(\chi_{9610}(7689, \cdot)\)	n/a	464	1
9610.2.e	\(\chi_{9610}(521, \cdot)\)	n/a	616	2
9610.2.f	\(\chi_{9610}(3843, \cdot)\)	n/a	928	2
9610.2.h	\(\chi_{9610}(531, \cdot)\)	n/a	1248	4
9610.2.k	\(\chi_{9610}(439, \cdot)\)	n/a	928	2
9610.2.n	\(\chi_{9610}(1349, \cdot)\)	n/a	1856	4
9610.2.p	\(\chi_{9610}(1483, \cdot)\)	n/a	1856	4
9610.2.q	\(\chi_{9610}(3221, \cdot)\)	n/a	2464	8
9610.2.s	\(\chi_{9610}(333, \cdot)\)	n/a	3712	8
9610.2.t	\(\chi_{9610}(1299, \cdot)\)	n/a	3712	8
9610.2.w	\(\chi_{9610}(311, \cdot)\)	n/a	9840	30
9610.2.x	\(\chi_{9610}(117, \cdot)\)	n/a	7424	16
9610.2.bb	\(\chi_{9610}(249, \cdot)\)	n/a	14880	30
9610.2.bc	\(\chi_{9610}(191, \cdot)\)	n/a	19920	60
9610.2.be	\(\chi_{9610}(123, \cdot)\)	n/a	29760	60
9610.2.bf	\(\chi_{9610}(101, \cdot)\)	n/a	39360	120
9610.2.bg	\(\chi_{9610}(129, \cdot)\)	n/a	29760	60
9610.2.bj	\(\chi_{9610}(39, \cdot)\)	n/a	59520	120
9610.2.bm	\(\chi_{9610}(37, \cdot)\)	n/a	59520	120
9610.2.bo	\(\chi_{9610}(41, \cdot)\)	n/a	79680	240
9610.2.bp	\(\chi_{9610}(23, \cdot)\)	n/a	119040	240
9610.2.bt	\(\chi_{9610}(9, \cdot)\)	n/a	119040	240
9610.2.bv	\(\chi_{9610}(3, \cdot)\)	n/a	238080	480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1922))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4805))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9610))\)\(^{\oplus 1}\)