Space of modular forms of level 7406 and weight 2

• Label: 7406.2
• Level: 7406
• Weight: 2
• Dimension: 533324
• Nonzero newspaces: 16
• Sturm bound: 6703488

Defining parameters

Level:	\( N \)	=	\( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(6703488\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7406))\).

	Total	New	Old
Modular forms	1684848	533324	1151524
Cusp forms	1666897	533324	1133573
Eisenstein series	17951	0	17951

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7406))\)

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
7406.2.a	\(\chi_{7406}(1, \cdot)\)	7406.2.a.a	1	1
		7406.2.a.b	1
		7406.2.a.c	1
		7406.2.a.d	1
		7406.2.a.e	1
		7406.2.a.f	1
		7406.2.a.g	1
		7406.2.a.h	1
		7406.2.a.i	1
		7406.2.a.j	2
		7406.2.a.k	2
		7406.2.a.l	2
		7406.2.a.m	2
		7406.2.a.n	2
		7406.2.a.o	2
		7406.2.a.p	2
		7406.2.a.q	2
		7406.2.a.r	2
		7406.2.a.s	2
		7406.2.a.t	3
		7406.2.a.u	3
		7406.2.a.v	3
		7406.2.a.w	3
		7406.2.a.x	3
		7406.2.a.y	4
		7406.2.a.z	4
		7406.2.a.ba	4
		7406.2.a.bb	4
		7406.2.a.bc	4
		7406.2.a.bd	4
		7406.2.a.be	5
		7406.2.a.bf	5
		7406.2.a.bg	5
		7406.2.a.bh	5
		7406.2.a.bi	6
		7406.2.a.bj	6
		7406.2.a.bk	6
		7406.2.a.bl	6
		7406.2.a.bm	8
		7406.2.a.bn	8
		7406.2.a.bo	10
		7406.2.a.bp	10
		7406.2.a.bq	12
		7406.2.a.br	12
		7406.2.a.bs	20
		7406.2.a.bt	20
		7406.2.a.bu	20
		7406.2.a.bv	20
7406.2.c	\(\chi_{7406}(7405, \cdot)\)	n/a	336	1
7406.2.e	\(\chi_{7406}(1059, \cdot)\)	n/a	672	2
7406.2.g	\(\chi_{7406}(4231, \cdot)\)	n/a	672	2
7406.2.i	\(\chi_{7406}(995, \cdot)\)	n/a	2520	10
7406.2.k	\(\chi_{7406}(195, \cdot)\)	n/a	3360	10
7406.2.m	\(\chi_{7406}(323, \cdot)\)	n/a	6072	22
7406.2.n	\(\chi_{7406}(177, \cdot)\)	n/a	6720	20
7406.2.p	\(\chi_{7406}(321, \cdot)\)	n/a	8096	22
7406.2.s	\(\chi_{7406}(411, \cdot)\)	n/a	6720	20
7406.2.u	\(\chi_{7406}(93, \cdot)\)	n/a	16192	44
7406.2.w	\(\chi_{7406}(45, \cdot)\)	n/a	16192	44
7406.2.y	\(\chi_{7406}(29, \cdot)\)	n/a	60720	220
7406.2.ba	\(\chi_{7406}(83, \cdot)\)	n/a	80960	220
7406.2.bc	\(\chi_{7406}(9, \cdot)\)	n/a	161920	440
7406.2.be	\(\chi_{7406}(5, \cdot)\)	n/a	161920	440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7406))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7406)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3703))\)\(^{\oplus 2}\)