Space of modular forms of level 6958 and weight 2

• Label: 6958.2
• Level: 6958
• Weight: 2
• Dimension: 473780
• Nonzero newspaces: 72
• Sturm bound: 5927040

Defining parameters

Level:	\( N \)	=	\( 6958 = 2 \cdot 7^{2} \cdot 71 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(5927040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6958))\).

	Total	New	Old
Modular forms	1490160	473780	1016380
Cusp forms	1473361	473780	999581
Eisenstein series	16799	0	16799

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6958))\)

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
6958.2.a	\(\chi_{6958}(1, \cdot)\)	6958.2.a.a	1	1
		6958.2.a.b	1
		6958.2.a.c	1
		6958.2.a.d	1
		6958.2.a.e	1
		6958.2.a.f	1
		6958.2.a.g	1
		6958.2.a.h	1
		6958.2.a.i	1
		6958.2.a.j	1
		6958.2.a.k	1
		6958.2.a.l	1
		6958.2.a.m	1
		6958.2.a.n	1
		6958.2.a.o	1
		6958.2.a.p	1
		6958.2.a.q	2
		6958.2.a.r	2
		6958.2.a.s	2
		6958.2.a.t	2
		6958.2.a.u	2
		6958.2.a.v	2
		6958.2.a.w	2
		6958.2.a.x	2
		6958.2.a.y	2
		6958.2.a.z	3
		6958.2.a.ba	3
		6958.2.a.bb	3
		6958.2.a.bc	3
		6958.2.a.bd	3
		6958.2.a.be	4
		6958.2.a.bf	4
		6958.2.a.bg	4
		6958.2.a.bh	6
		6958.2.a.bi	7
		6958.2.a.bj	8
		6958.2.a.bk	8
		6958.2.a.bl	9
		6958.2.a.bm	9
		6958.2.a.bn	10
		6958.2.a.bo	10
		6958.2.a.bp	10
		6958.2.a.bq	11
		6958.2.a.br	11
		6958.2.a.bs	12
		6958.2.a.bt	12
		6958.2.a.bu	12
		6958.2.a.bv	12
		6958.2.a.bw	16
		6958.2.a.bx	16
6958.2.b	\(\chi_{6958}(6957, \cdot)\)	n/a	240	1
6958.2.e	\(\chi_{6958}(569, \cdot)\)	n/a	464	2
6958.2.f	\(\chi_{6958}(2255, \cdot)\)	n/a	984	4
6958.2.i	\(\chi_{6958}(3265, \cdot)\)	n/a	480	2
6958.2.j	\(\chi_{6958}(3445, \cdot)\)	n/a	2016	6
6958.2.k	\(\chi_{6958}(953, \cdot)\)	n/a	2016	6
6958.2.l	\(\chi_{6958}(1653, \cdot)\)	n/a	2016	6
6958.2.m	\(\chi_{6958}(995, \cdot)\)	n/a	1944	6
6958.2.n	\(\chi_{6958}(659, \cdot)\)	n/a	2016	6
6958.2.o	\(\chi_{6958}(897, \cdot)\)	n/a	2016	6
6958.2.p	\(\chi_{6958}(687, \cdot)\)	n/a	1476	6
6958.2.q	\(\chi_{6958}(463, \cdot)\)	n/a	2016	6
6958.2.t	\(\chi_{6958}(685, \cdot)\)	n/a	960	4
6958.2.v	\(\chi_{6958}(1091, \cdot)\)	n/a	2016	6
6958.2.be	\(\chi_{6958}(97, \cdot)\)	n/a	1440	6
6958.2.bf	\(\chi_{6958}(335, \cdot)\)	n/a	2016	6
6958.2.bl	\(\chi_{6958}(993, \cdot)\)	n/a	2016	6
6958.2.bm	\(\chi_{6958}(307, \cdot)\)	n/a	2016	6
6958.2.bn	\(\chi_{6958}(531, \cdot)\)	n/a	2016	6
6958.2.bo	\(\chi_{6958}(181, \cdot)\)	n/a	2016	6
6958.2.bp	\(\chi_{6958}(41, \cdot)\)	n/a	2016	6
6958.2.bs	\(\chi_{6958}(2419, \cdot)\)	n/a	1920	8
6958.2.bt	\(\chi_{6958}(387, \cdot)\)	n/a	4032	12
6958.2.bu	\(\chi_{6958}(471, \cdot)\)	n/a	2880	12
6958.2.bv	\(\chi_{6958}(37, \cdot)\)	n/a	4032	12
6958.2.bw	\(\chi_{6958}(711, \cdot)\)	n/a	3936	12
6958.2.bx	\(\chi_{6958}(233, \cdot)\)	n/a	4032	12
6958.2.by	\(\chi_{6958}(261, \cdot)\)	n/a	4032	12
6958.2.bz	\(\chi_{6958}(527, \cdot)\)	n/a	4032	12
6958.2.ca	\(\chi_{6958}(1031, \cdot)\)	n/a	4032	12
6958.2.cb	\(\chi_{6958}(117, \cdot)\)	n/a	1920	8
6958.2.ce	\(\chi_{6958}(365, \cdot)\)	n/a	8064	24
6958.2.cf	\(\chi_{6958}(393, \cdot)\)	n/a	5904	24
6958.2.cg	\(\chi_{6958}(169, \cdot)\)	n/a	8064	24
6958.2.ch	\(\chi_{6958}(253, \cdot)\)	n/a	8064	24
6958.2.ci	\(\chi_{6958}(57, \cdot)\)	n/a	8064	24
6958.2.cj	\(\chi_{6958}(43, \cdot)\)	n/a	8064	24
6958.2.ck	\(\chi_{6958}(29, \cdot)\)	n/a	8064	24
6958.2.cl	\(\chi_{6958}(15, \cdot)\)	n/a	8064	24
6958.2.co	\(\chi_{6958}(733, \cdot)\)	n/a	4032	12
6958.2.cp	\(\chi_{6958}(467, \cdot)\)	n/a	4032	12
6958.2.cq	\(\chi_{6958}(465, \cdot)\)	n/a	4032	12
6958.2.cr	\(\chi_{6958}(283, \cdot)\)	n/a	4032	12
6958.2.cs	\(\chi_{6958}(523, \cdot)\)	n/a	4032	12
6958.2.cy	\(\chi_{6958}(1601, \cdot)\)	n/a	4032	12
6958.2.cz	\(\chi_{6958}(325, \cdot)\)	n/a	2880	12
6958.2.di	\(\chi_{6958}(381, \cdot)\)	n/a	4032	12
6958.2.dm	\(\chi_{6958}(55, \cdot)\)	n/a	8064	24
6958.2.dn	\(\chi_{6958}(209, \cdot)\)	n/a	8064	24
6958.2.do	\(\chi_{6958}(349, \cdot)\)	n/a	8064	24
6958.2.dp	\(\chi_{6958}(559, \cdot)\)	n/a	8064	24
6958.2.dq	\(\chi_{6958}(279, \cdot)\)	n/a	8064	24
6958.2.dw	\(\chi_{6958}(13, \cdot)\)	n/a	8064	24
6958.2.dx	\(\chi_{6958}(195, \cdot)\)	n/a	5760	24
6958.2.eg	\(\chi_{6958}(461, \cdot)\)	n/a	8064	24
6958.2.ei	\(\chi_{6958}(107, \cdot)\)	n/a	16128	48
6958.2.ej	\(\chi_{6958}(151, \cdot)\)	n/a	16128	48
6958.2.ek	\(\chi_{6958}(109, \cdot)\)	n/a	16128	48
6958.2.el	\(\chi_{6958}(219, \cdot)\)	n/a	16128	48
6958.2.em	\(\chi_{6958}(25, \cdot)\)	n/a	16128	48
6958.2.en	\(\chi_{6958}(9, \cdot)\)	n/a	16128	48
6958.2.eo	\(\chi_{6958}(79, \cdot)\)	n/a	11520	48
6958.2.ep	\(\chi_{6958}(95, \cdot)\)	n/a	16128	48
6958.2.er	\(\chi_{6958}(115, \cdot)\)	n/a	16128	48
6958.2.fa	\(\chi_{6958}(31, \cdot)\)	n/a	11520	48
6958.2.fb	\(\chi_{6958}(61, \cdot)\)	n/a	16128	48
6958.2.fh	\(\chi_{6958}(59, \cdot)\)	n/a	16128	48
6958.2.fi	\(\chi_{6958}(17, \cdot)\)	n/a	16128	48
6958.2.fj	\(\chi_{6958}(339, \cdot)\)	n/a	16128	48
6958.2.fk	\(\chi_{6958}(201, \cdot)\)	n/a	16128	48
6958.2.fl	\(\chi_{6958}(33, \cdot)\)	n/a	16128	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6958))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6958)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(142))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(497))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(994))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3479))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6958))\)\(^{\oplus 1}\)