Space of modular forms of level 6422 and weight 2

• Label: 6422.2
• Level: 6422
• Weight: 2
• Dimension: 418515
• Nonzero newspaces: 48
• Sturm bound: 5110560

Defining parameters

Level:	\( N \)	=	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(5110560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6422))\).

	Total	New	Old
Modular forms	1285848	418515	867333
Cusp forms	1269433	418515	850918
Eisenstein series	16415	0	16415

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6422))\)

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
6422.2.a	\(\chi_{6422}(1, \cdot)\)	6422.2.a.a	1	1
		6422.2.a.b	1
		6422.2.a.c	1
		6422.2.a.d	1
		6422.2.a.e	1
		6422.2.a.f	1
		6422.2.a.g	1
		6422.2.a.h	1
		6422.2.a.i	1
		6422.2.a.j	1
		6422.2.a.k	3
		6422.2.a.l	3
		6422.2.a.m	3
		6422.2.a.n	3
		6422.2.a.o	3
		6422.2.a.p	3
		6422.2.a.q	3
		6422.2.a.r	3
		6422.2.a.s	3
		6422.2.a.t	3
		6422.2.a.u	3
		6422.2.a.v	3
		6422.2.a.w	3
		6422.2.a.x	3
		6422.2.a.y	3
		6422.2.a.z	4
		6422.2.a.ba	4
		6422.2.a.bb	4
		6422.2.a.bc	6
		6422.2.a.bd	6
		6422.2.a.be	7
		6422.2.a.bf	7
		6422.2.a.bg	8
		6422.2.a.bh	8
		6422.2.a.bi	9
		6422.2.a.bj	9
		6422.2.a.bk	9
		6422.2.a.bl	9
		6422.2.a.bm	14
		6422.2.a.bn	14
		6422.2.a.bo	15
		6422.2.a.bp	15
		6422.2.a.bq	15
		6422.2.a.br	15
6422.2.d	\(\chi_{6422}(3041, \cdot)\)	n/a	230	1
6422.2.e	\(\chi_{6422}(653, \cdot)\)	n/a	516	2
6422.2.f	\(\chi_{6422}(2367, \cdot)\)	n/a	514	2
6422.2.g	\(\chi_{6422}(191, \cdot)\)	n/a	464	2
6422.2.h	\(\chi_{6422}(315, \cdot)\)	n/a	516	2
6422.2.i	\(\chi_{6422}(1253, \cdot)\)	n/a	508	2
6422.2.m	\(\chi_{6422}(2851, \cdot)\)	n/a	460	2
6422.2.n	\(\chi_{6422}(5407, \cdot)\)	n/a	508	2
6422.2.o	\(\chi_{6422}(1375, \cdot)\)	n/a	516	2
6422.2.v	\(\chi_{6422}(1037, \cdot)\)	n/a	516	2
6422.2.w	\(\chi_{6422}(529, \cdot)\)	n/a	1536	6
6422.2.x	\(\chi_{6422}(339, \cdot)\)	n/a	1554	6
6422.2.y	\(\chi_{6422}(1543, \cdot)\)	n/a	1536	6
6422.2.z	\(\chi_{6422}(2117, \cdot)\)	n/a	1032	4
6422.2.bd	\(\chi_{6422}(1779, \cdot)\)	n/a	1032	4
6422.2.be	\(\chi_{6422}(1671, \cdot)\)	n/a	1032	4
6422.2.bf	\(\chi_{6422}(4971, \cdot)\)	n/a	1016	4
6422.2.bh	\(\chi_{6422}(495, \cdot)\)	n/a	3264	12
6422.2.bi	\(\chi_{6422}(823, \cdot)\)	n/a	1536	6
6422.2.bm	\(\chi_{6422}(1013, \cdot)\)	n/a	1548	6
6422.2.bn	\(\chi_{6422}(23, \cdot)\)	n/a	1536	6
6422.2.br	\(\chi_{6422}(77, \cdot)\)	n/a	3288	12
6422.2.bx	\(\chi_{6422}(249, \cdot)\)	n/a	3072	12
6422.2.by	\(\chi_{6422}(89, \cdot)\)	n/a	3072	12
6422.2.bz	\(\chi_{6422}(775, \cdot)\)	n/a	3096	12
6422.2.ca	\(\chi_{6422}(425, \cdot)\)	n/a	7248	24
6422.2.cb	\(\chi_{6422}(419, \cdot)\)	n/a	6528	24
6422.2.cc	\(\chi_{6422}(235, \cdot)\)	n/a	7344	24
6422.2.cd	\(\chi_{6422}(87, \cdot)\)	n/a	7248	24
6422.2.cf	\(\chi_{6422}(151, \cdot)\)	n/a	7344	24
6422.2.cg	\(\chi_{6422}(49, \cdot)\)	n/a	7248	24
6422.2.cn	\(\chi_{6422}(277, \cdot)\)	n/a	7248	24
6422.2.co	\(\chi_{6422}(311, \cdot)\)	n/a	7344	24
6422.2.cp	\(\chi_{6422}(153, \cdot)\)	n/a	6576	24
6422.2.cs	\(\chi_{6422}(9, \cdot)\)	n/a	21888	72
6422.2.ct	\(\chi_{6422}(131, \cdot)\)	n/a	21744	72
6422.2.cu	\(\chi_{6422}(35, \cdot)\)	n/a	21888	72
6422.2.cw	\(\chi_{6422}(31, \cdot)\)	n/a	14688	48
6422.2.cx	\(\chi_{6422}(37, \cdot)\)	n/a	14496	48
6422.2.cy	\(\chi_{6422}(145, \cdot)\)	n/a	14496	48
6422.2.dc	\(\chi_{6422}(141, \cdot)\)	n/a	14496	48
6422.2.dg	\(\chi_{6422}(17, \cdot)\)	n/a	21888	72
6422.2.dh	\(\chi_{6422}(25, \cdot)\)	n/a	21744	72
6422.2.dl	\(\chi_{6422}(199, \cdot)\)	n/a	21888	72
6422.2.dm	\(\chi_{6422}(21, \cdot)\)	n/a	43488	144
6422.2.dn	\(\chi_{6422}(15, \cdot)\)	n/a	43776	144
6422.2.do	\(\chi_{6422}(41, \cdot)\)	n/a	43776	144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6422))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6422)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(494))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3211))\)\(^{\oplus 2}\)