Space of modular forms of level 6348 and weight 2

• Label: 6348.2
• Level: 6348
• Weight: 2
• Dimension: 485540
• Nonzero newspaces: 16
• Sturm bound: 4468992

Defining parameters

Level:	\( N \)	=	\( 6348 = 2^{2} \cdot 3 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(4468992\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6348))\).

	Total	New	Old
Modular forms	1124728	488360	636368
Cusp forms	1109769	485540	624229
Eisenstein series	14959	2820	12139

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6348))\)

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
6348.2.a	\(\chi_{6348}(1, \cdot)\)	6348.2.a.a	1	1
		6348.2.a.b	1
		6348.2.a.c	1
		6348.2.a.d	1
		6348.2.a.e	2
		6348.2.a.f	2
		6348.2.a.g	2
		6348.2.a.h	2
		6348.2.a.i	2
		6348.2.a.j	2
		6348.2.a.k	3
		6348.2.a.l	3
		6348.2.a.m	4
		6348.2.a.n	4
		6348.2.a.o	6
		6348.2.a.p	8
		6348.2.a.q	10
		6348.2.a.r	10
		6348.2.a.s	10
		6348.2.a.t	10
6348.2.c	\(\chi_{6348}(5291, \cdot)\)	n/a	968	1
6348.2.e	\(\chi_{6348}(4231, \cdot)\)	n/a	504	1
6348.2.g	\(\chi_{6348}(3173, \cdot)\)	n/a	168	1
6348.2.i	\(\chi_{6348}(1705, \cdot)\)	n/a	840	10
6348.2.k	\(\chi_{6348}(557, \cdot)\)	n/a	1680	10
6348.2.m	\(\chi_{6348}(571, \cdot)\)	n/a	5040	10
6348.2.o	\(\chi_{6348}(647, \cdot)\)	n/a	9680	10
6348.2.q	\(\chi_{6348}(277, \cdot)\)	n/a	2024	22
6348.2.s	\(\chi_{6348}(137, \cdot)\)	n/a	4048	22
6348.2.u	\(\chi_{6348}(91, \cdot)\)	n/a	12144	22
6348.2.w	\(\chi_{6348}(47, \cdot)\)	n/a	24200	22
6348.2.y	\(\chi_{6348}(13, \cdot)\)	n/a	20240	220
6348.2.ba	\(\chi_{6348}(35, \cdot)\)	n/a	242000	220
6348.2.bc	\(\chi_{6348}(7, \cdot)\)	n/a	121440	220
6348.2.be	\(\chi_{6348}(5, \cdot)\)	n/a	40480	220

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6348))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6348)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1587))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3174))\)\(^{\oplus 2}\)