Space of modular forms of level 8214 and weight 2

• Label: 8214.2
• Level: 8214
• Weight: 2
• Dimension: 467513
• Nonzero newspaces: 18
• Sturm bound: 7491168

Defining parameters

Level:	\( N \)	=	\( 8214 = 2 \cdot 3 \cdot 37^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(7491168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8214))\).

	Total	New	Old
Modular forms	1880712	467513	1413199
Cusp forms	1864873	467513	1397360
Eisenstein series	15839	0	15839

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8214))\)

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
8214.2.a	\(\chi_{8214}(1, \cdot)\)	8214.2.a.a	1	1
		8214.2.a.b	1
		8214.2.a.c	1
		8214.2.a.d	1
		8214.2.a.e	1
		8214.2.a.f	1
		8214.2.a.g	1
		8214.2.a.h	1
		8214.2.a.i	1
		8214.2.a.j	1
		8214.2.a.k	1
		8214.2.a.l	2
		8214.2.a.m	2
		8214.2.a.n	2
		8214.2.a.o	2
		8214.2.a.p	2
		8214.2.a.q	2
		8214.2.a.r	3
		8214.2.a.s	3
		8214.2.a.t	3
		8214.2.a.u	3
		8214.2.a.v	3
		8214.2.a.w	3
		8214.2.a.x	3
		8214.2.a.y	3
		8214.2.a.z	4
		8214.2.a.ba	4
		8214.2.a.bb	6
		8214.2.a.bc	6
		8214.2.a.bd	9
		8214.2.a.be	9
		8214.2.a.bf	9
		8214.2.a.bg	9
		8214.2.a.bh	12
		8214.2.a.bi	12
		8214.2.a.bj	12
		8214.2.a.bk	12
		8214.2.a.bl	18
		8214.2.a.bm	18
		8214.2.a.bn	18
		8214.2.a.bo	18
8214.2.c	\(\chi_{8214}(2737, \cdot)\)	n/a	222	1
8214.2.e	\(\chi_{8214}(787, \cdot)\)	n/a	448	2
8214.2.g	\(\chi_{8214}(2621, \cdot)\)	n/a	884	2
8214.2.j	\(\chi_{8214}(1951, \cdot)\)	n/a	444	2
8214.2.k	\(\chi_{8214}(1015, \cdot)\)	n/a	1332	6
8214.2.m	\(\chi_{8214}(473, \cdot)\)	n/a	1768	4
8214.2.n	\(\chi_{8214}(691, \cdot)\)	n/a	1320	6
8214.2.q	\(\chi_{8214}(875, \cdot)\)	n/a	5328	12
8214.2.s	\(\chi_{8214}(223, \cdot)\)	n/a	8352	36
8214.2.u	\(\chi_{8214}(73, \cdot)\)	n/a	8424	36
8214.2.w	\(\chi_{8214}(121, \cdot)\)	n/a	16704	72
8214.2.x	\(\chi_{8214}(179, \cdot)\)	n/a	33840	72
8214.2.z	\(\chi_{8214}(85, \cdot)\)	n/a	16848	72
8214.2.bc	\(\chi_{8214}(7, \cdot)\)	n/a	50544	216
8214.2.bd	\(\chi_{8214}(23, \cdot)\)	n/a	67680	144
8214.2.bh	\(\chi_{8214}(25, \cdot)\)	n/a	50976	216
8214.2.bj	\(\chi_{8214}(5, \cdot)\)	n/a	202176	432

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8214))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8214)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2738))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4107))\)\(^{\oplus 2}\)