Space of modular forms of level 7942 and weight 2

• Label: 7942.2
• Level: 7942
• Weight: 2
• Dimension: 635433
• Nonzero newspaces: 24
• Sturm bound: 7797600

Defining parameters

Level:	\( N \)	=	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(7797600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7942))\).

	Total	New	Old
Modular forms	1959480	635433	1324047
Cusp forms	1939321	635433	1303888
Eisenstein series	20159	0	20159

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7942))\)

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
7942.2.a	\(\chi_{7942}(1, \cdot)\)	7942.2.a.a	1	1
		7942.2.a.b	1
		7942.2.a.c	1
		7942.2.a.d	1
		7942.2.a.e	1
		7942.2.a.f	1
		7942.2.a.g	1
		7942.2.a.h	1
		7942.2.a.i	1
		7942.2.a.j	1
		7942.2.a.k	1
		7942.2.a.l	1
		7942.2.a.m	1
		7942.2.a.n	1
		7942.2.a.o	1
		7942.2.a.p	1
		7942.2.a.q	1
		7942.2.a.r	1
		7942.2.a.s	1
		7942.2.a.t	2
		7942.2.a.u	2
		7942.2.a.v	2
		7942.2.a.w	2
		7942.2.a.x	2
		7942.2.a.y	2
		7942.2.a.z	2
		7942.2.a.ba	2
		7942.2.a.bb	2
		7942.2.a.bc	3
		7942.2.a.bd	3
		7942.2.a.be	3
		7942.2.a.bf	3
		7942.2.a.bg	3
		7942.2.a.bh	3
		7942.2.a.bi	3
		7942.2.a.bj	3
		7942.2.a.bk	6
		7942.2.a.bl	6
		7942.2.a.bm	8
		7942.2.a.bn	8
		7942.2.a.bo	8
		7942.2.a.bp	8
		7942.2.a.bq	8
		7942.2.a.br	8
		7942.2.a.bs	12
		7942.2.a.bt	12
		7942.2.a.bu	12
		7942.2.a.bv	12
		7942.2.a.bw	12
		7942.2.a.bx	12
		7942.2.a.by	15
		7942.2.a.bz	15
		7942.2.a.ca	15
		7942.2.a.cb	15
		7942.2.a.cc	16
		7942.2.a.cd	16
7942.2.b	\(\chi_{7942}(7941, \cdot)\)	n/a	340	1
7942.2.e	\(\chi_{7942}(6205, \cdot)\)	n/a	572	2
7942.2.f	\(\chi_{7942}(1445, \cdot)\)	n/a	1364	4
7942.2.h	\(\chi_{7942}(791, \cdot)\)	n/a	680	2
7942.2.j	\(\chi_{7942}(595, \cdot)\)	n/a	1692	6
7942.2.m	\(\chi_{7942}(721, \cdot)\)	n/a	1360	4
7942.2.n	\(\chi_{7942}(653, \cdot)\)	n/a	2720	8
7942.2.q	\(\chi_{7942}(307, \cdot)\)	n/a	2040	6
7942.2.r	\(\chi_{7942}(419, \cdot)\)	n/a	5652	18
7942.2.t	\(\chi_{7942}(293, \cdot)\)	n/a	2720	8
7942.2.x	\(\chi_{7942}(417, \cdot)\)	n/a	6840	18
7942.2.y	\(\chi_{7942}(245, \cdot)\)	n/a	8160	24
7942.2.z	\(\chi_{7942}(45, \cdot)\)	n/a	11304	36
7942.2.ba	\(\chi_{7942}(127, \cdot)\)	n/a	8160	24
7942.2.bd	\(\chi_{7942}(115, \cdot)\)	n/a	27360	72
7942.2.bf	\(\chi_{7942}(65, \cdot)\)	n/a	13680	36
7942.2.bh	\(\chi_{7942}(23, \cdot)\)	n/a	34344	108
7942.2.bi	\(\chi_{7942}(151, \cdot)\)	n/a	27360	72
7942.2.bl	\(\chi_{7942}(49, \cdot)\)	n/a	54720	144
7942.2.bm	\(\chi_{7942}(21, \cdot)\)	n/a	41040	108
7942.2.bq	\(\chi_{7942}(107, \cdot)\)	n/a	54720	144
7942.2.bs	\(\chi_{7942}(5, \cdot)\)	n/a	164160	432
7942.2.bv	\(\chi_{7942}(13, \cdot)\)	n/a	164160	432

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7942))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7942)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3971))\)\(^{\oplus 2}\)