Space of modular forms of level 12482 and weight 2

• Label: 12482.2
• Level: 12482
• Weight: 2
• Dimension: 1622141
• Nonzero newspaces: 8
• Sturm bound: 19471920

Defining parameters

Level:	\( N \)	=	\( 12482 = 2 \cdot 79^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(19471920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(12482))\).

	Total	New	Old
Modular forms	4877184	1622141	3255043
Cusp forms	4858777	1622141	3236636
Eisenstein series	18407	0	18407

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(12482))\)

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
12482.2.a	\(\chi_{12482}(1, \cdot)\)	12482.2.a.a	1	1
		12482.2.a.b	1
		12482.2.a.c	1
		12482.2.a.d	1
		12482.2.a.e	1
		12482.2.a.f	1
		12482.2.a.g	1
		12482.2.a.h	1
		12482.2.a.i	1
		12482.2.a.j	2
		12482.2.a.k	2
		12482.2.a.l	2
		12482.2.a.m	2
		12482.2.a.n	2
		12482.2.a.o	2
		12482.2.a.p	2
		12482.2.a.q	2
		12482.2.a.r	2
		12482.2.a.s	2
		12482.2.a.t	2
		12482.2.a.u	2
		12482.2.a.v	2
		12482.2.a.w	2
		12482.2.a.x	4
		12482.2.a.y	4
		12482.2.a.z	4
		12482.2.a.ba	4
		12482.2.a.bb	4
		12482.2.a.bc	6
		12482.2.a.bd	6
		12482.2.a.be	8
		12482.2.a.bf	12
		12482.2.a.bg	16
		12482.2.a.bh	16
		12482.2.a.bi	16
		12482.2.a.bj	24
		12482.2.a.bk	24
		12482.2.a.bl	24
		12482.2.a.bm	24
		12482.2.a.bn	24
		12482.2.a.bo	36
		12482.2.a.bp	36
		12482.2.a.bq	36
		12482.2.a.br	36
		12482.2.a.bs	48
		12482.2.a.bt	64
12482.2.c	\(\chi_{12482}(7955, \cdot)\)	n/a	1028	2
12482.2.e	\(\chi_{12482}(1127, \cdot)\)	n/a	6144	12
12482.2.g	\(\chi_{12482}(31, \cdot)\)	n/a	12336	24
12482.2.i	\(\chi_{12482}(159, \cdot)\)	n/a	41184	78
12482.2.k	\(\chi_{12482}(23, \cdot)\)	n/a	82056	156
12482.2.m	\(\chi_{12482}(21, \cdot)\)	n/a	494208	936
12482.2.o	\(\chi_{12482}(5, \cdot)\)	n/a	984672	1872

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(12482))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(12482)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6241))\)\(^{\oplus 2}\)