Space of modular forms of level 6354 and weight 2

• Label: 6354.2
• Level: 6354
• Weight: 2
• Dimension: 295940
• Nonzero newspaces: 24
• Sturm bound: 4485888

Defining parameters

Level:	\( N \)	=	\( 6354 = 2 \cdot 3^{2} \cdot 353 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(4485888\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6354))\).

	Total	New	Old
Modular forms	1127104	295940	831164
Cusp forms	1115841	295940	819901
Eisenstein series	11263	0	11263

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6354))\)

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
6354.2.a	\(\chi_{6354}(1, \cdot)\)	6354.2.a.a	1	1
		6354.2.a.b	1
		6354.2.a.c	1
		6354.2.a.d	1
		6354.2.a.e	1
		6354.2.a.f	1
		6354.2.a.g	1
		6354.2.a.h	1
		6354.2.a.i	1
		6354.2.a.j	1
		6354.2.a.k	1
		6354.2.a.l	1
		6354.2.a.m	1
		6354.2.a.n	1
		6354.2.a.o	1
		6354.2.a.p	1
		6354.2.a.q	1
		6354.2.a.r	1
		6354.2.a.s	2
		6354.2.a.t	2
		6354.2.a.u	2
		6354.2.a.v	2
		6354.2.a.w	2
		6354.2.a.x	2
		6354.2.a.y	2
		6354.2.a.z	2
		6354.2.a.ba	3
		6354.2.a.bb	3
		6354.2.a.bc	3
		6354.2.a.bd	5
		6354.2.a.be	5
		6354.2.a.bf	5
		6354.2.a.bg	6
		6354.2.a.bh	7
		6354.2.a.bi	8
		6354.2.a.bj	9
		6354.2.a.bk	10
		6354.2.a.bl	10
		6354.2.a.bm	20
		6354.2.a.bn	20
6354.2.b	\(\chi_{6354}(3529, \cdot)\)	n/a	148	1
6354.2.e	\(\chi_{6354}(2119, \cdot)\)	n/a	704	2
6354.2.g	\(\chi_{6354}(3925, \cdot)\)	n/a	296	2
6354.2.j	\(\chi_{6354}(1411, \cdot)\)	n/a	708	2
6354.2.k	\(\chi_{6354}(469, \cdot)\)	n/a	592	4
6354.2.m	\(\chi_{6354}(217, \cdot)\)	n/a	1480	10
6354.2.n	\(\chi_{6354}(1723, \cdot)\)	n/a	1416	4
6354.2.p	\(\chi_{6354}(253, \cdot)\)	n/a	1176	8
6354.2.s	\(\chi_{6354}(919, \cdot)\)	n/a	1480	10
6354.2.v	\(\chi_{6354}(283, \cdot)\)	n/a	2832	8
6354.2.w	\(\chi_{6354}(359, \cdot)\)	n/a	1888	16
6354.2.y	\(\chi_{6354}(187, \cdot)\)	n/a	7080	20
6354.2.z	\(\chi_{6354}(289, \cdot)\)	n/a	2960	20
6354.2.bb	\(\chi_{6354}(49, \cdot)\)	n/a	5664	16
6354.2.be	\(\chi_{6354}(97, \cdot)\)	n/a	7080	20
6354.2.bh	\(\chi_{6354}(73, \cdot)\)	n/a	5920	40
6354.2.bj	\(\chi_{6354}(59, \cdot)\)	n/a	11328	32
6354.2.bl	\(\chi_{6354}(121, \cdot)\)	n/a	14160	40
6354.2.bn	\(\chi_{6354}(19, \cdot)\)	n/a	11760	80
6354.2.bo	\(\chi_{6354}(61, \cdot)\)	n/a	28320	80
6354.2.br	\(\chi_{6354}(53, \cdot)\)	n/a	18880	160
6354.2.bt	\(\chi_{6354}(25, \cdot)\)	n/a	56640	160
6354.2.bu	\(\chi_{6354}(5, \cdot)\)	n/a	113280	320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6354))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6354)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(353))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(706))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1059))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3177))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6354))\)\(^{\oplus 1}\)