Space of modular forms of level 6848 and weight 2

• Label: 6848.2
• Level: 6848
• Weight: 2
• Dimension: 821802
• Nonzero newspaces: 16
• Sturm bound: 5861376

Defining parameters

Level:	\( N \)	=	\( 6848 = 2^{6} \cdot 107 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(5861376\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6848))\).

	Total	New	Old
Modular forms	1472976	826422	646554
Cusp forms	1457713	821802	635911
Eisenstein series	15263	4620	10643

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6848))\)

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
6848.2.a	\(\chi_{6848}(1, \cdot)\)	6848.2.a.a	1	1
		6848.2.a.b	1
		6848.2.a.c	1
		6848.2.a.d	1
		6848.2.a.e	1
		6848.2.a.f	1
		6848.2.a.g	1
		6848.2.a.h	1
		6848.2.a.i	1
		6848.2.a.j	1
		6848.2.a.k	1
		6848.2.a.l	1
		6848.2.a.m	1
		6848.2.a.n	1
		6848.2.a.o	1
		6848.2.a.p	1
		6848.2.a.q	1
		6848.2.a.r	1
		6848.2.a.s	1
		6848.2.a.t	1
		6848.2.a.u	1
		6848.2.a.v	1
		6848.2.a.w	1
		6848.2.a.x	1
		6848.2.a.y	2
		6848.2.a.z	2
		6848.2.a.ba	2
		6848.2.a.bb	2
		6848.2.a.bc	2
		6848.2.a.bd	2
		6848.2.a.be	2
		6848.2.a.bf	2
		6848.2.a.bg	2
		6848.2.a.bh	2
		6848.2.a.bi	2
		6848.2.a.bj	2
		6848.2.a.bk	2
		6848.2.a.bl	2
		6848.2.a.bm	2
		6848.2.a.bn	2
		6848.2.a.bo	3
		6848.2.a.bp	3
		6848.2.a.bq	5
		6848.2.a.br	5
		6848.2.a.bs	6
		6848.2.a.bt	6
		6848.2.a.bu	7
		6848.2.a.bv	7
		6848.2.a.bw	10
		6848.2.a.bx	10
		6848.2.a.by	10
		6848.2.a.bz	10
		6848.2.a.ca	12
		6848.2.a.cb	12
		6848.2.a.cc	12
		6848.2.a.cd	12
		6848.2.a.ce	13
		6848.2.a.cf	13
6848.2.b	\(\chi_{6848}(3425, \cdot)\)	n/a	212	1
6848.2.c	\(\chi_{6848}(6847, \cdot)\)	n/a	214	1
6848.2.h	\(\chi_{6848}(3423, \cdot)\)	n/a	216	1
6848.2.i	\(\chi_{6848}(1711, \cdot)\)	n/a	428	2
6848.2.j	\(\chi_{6848}(1713, \cdot)\)	n/a	424	2
6848.2.m	\(\chi_{6848}(857, \cdot)\)	None	0	4
6848.2.n	\(\chi_{6848}(855, \cdot)\)	None	0	4
6848.2.q	\(\chi_{6848}(427, \cdot)\)	n/a	6896	8
6848.2.r	\(\chi_{6848}(429, \cdot)\)	n/a	6784	8
6848.2.u	\(\chi_{6848}(193, \cdot)\)	n/a	11128	52
6848.2.v	\(\chi_{6848}(31, \cdot)\)	n/a	11232	52
6848.2.ba	\(\chi_{6848}(63, \cdot)\)	n/a	11128	52
6848.2.bb	\(\chi_{6848}(33, \cdot)\)	n/a	11232	52
6848.2.be	\(\chi_{6848}(49, \cdot)\)	n/a	22256	104
6848.2.bf	\(\chi_{6848}(15, \cdot)\)	n/a	22256	104
6848.2.bi	\(\chi_{6848}(7, \cdot)\)	None	0	208
6848.2.bj	\(\chi_{6848}(9, \cdot)\)	None	0	208
6848.2.bm	\(\chi_{6848}(13, \cdot)\)	n/a	358592	416
6848.2.bn	\(\chi_{6848}(43, \cdot)\)	n/a	358592	416

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6848))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6848)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(107))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(214))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(428))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(856))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1712))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3424))\)\(^{\oplus 2}\)