Space of modular forms of level 6897 and weight 2

• Label: 6897.2
• Level: 6897
• Weight: 2
• Dimension: 1273370
• Nonzero newspaces: 48
• Sturm bound: 6969600

Defining parameters

Level:	\( N \)	=	\( 6897 = 3 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(6969600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6897))\).

	Total	New	Old
Modular forms	1753920	1282926	470994
Cusp forms	1730881	1273370	457511
Eisenstein series	23039	9556	13483

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6897))\)

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
6897.2.a	\(\chi_{6897}(1, \cdot)\)	6897.2.a.a	1	1
		6897.2.a.b	1
		6897.2.a.c	1
		6897.2.a.d	1
		6897.2.a.e	1
		6897.2.a.f	1
		6897.2.a.g	1
		6897.2.a.h	2
		6897.2.a.i	2
		6897.2.a.j	2
		6897.2.a.k	2
		6897.2.a.l	3
		6897.2.a.m	3
		6897.2.a.n	3
		6897.2.a.o	3
		6897.2.a.p	3
		6897.2.a.q	4
		6897.2.a.r	5
		6897.2.a.s	5
		6897.2.a.t	6
		6897.2.a.u	6
		6897.2.a.v	6
		6897.2.a.w	6
		6897.2.a.x	6
		6897.2.a.y	6
		6897.2.a.z	7
		6897.2.a.ba	7
		6897.2.a.bb	8
		6897.2.a.bc	8
		6897.2.a.bd	8
		6897.2.a.be	8
		6897.2.a.bf	12
		6897.2.a.bg	12
		6897.2.a.bh	14
		6897.2.a.bi	14
		6897.2.a.bj	14
		6897.2.a.bk	14
		6897.2.a.bl	16
		6897.2.a.bm	16
		6897.2.a.bn	20
		6897.2.a.bo	20
		6897.2.a.bp	24
		6897.2.a.bq	24
6897.2.f	\(\chi_{6897}(362, \cdot)\)	n/a	648	1
6897.2.g	\(\chi_{6897}(1937, \cdot)\)	n/a	708	1
6897.2.h	\(\chi_{6897}(4597, \cdot)\)	n/a	360	1
6897.2.i	\(\chi_{6897}(1090, \cdot)\)	n/a	728	2
6897.2.j	\(\chi_{6897}(856, \cdot)\)	n/a	1296	4
6897.2.k	\(\chi_{6897}(2782, \cdot)\)	n/a	720	2
6897.2.l	\(\chi_{6897}(1451, \cdot)\)	n/a	1408	2
6897.2.m	\(\chi_{6897}(122, \cdot)\)	n/a	1416	2
6897.2.r	\(\chi_{6897}(727, \cdot)\)	n/a	2178	6
6897.2.s	\(\chi_{6897}(94, \cdot)\)	n/a	1440	4
6897.2.t	\(\chi_{6897}(2792, \cdot)\)	n/a	2816	4
6897.2.u	\(\chi_{6897}(2756, \cdot)\)	n/a	2592	4
6897.2.z	\(\chi_{6897}(628, \cdot)\)	n/a	3960	10
6897.2.ba	\(\chi_{6897}(1945, \cdot)\)	n/a	2880	8
6897.2.bb	\(\chi_{6897}(485, \cdot)\)	n/a	4254	6
6897.2.be	\(\chi_{6897}(1088, \cdot)\)	n/a	4224	6
6897.2.bf	\(\chi_{6897}(241, \cdot)\)	n/a	2160	6
6897.2.bi	\(\chi_{6897}(208, \cdot)\)	n/a	4400	10
6897.2.bj	\(\chi_{6897}(56, \cdot)\)	n/a	8760	10
6897.2.bk	\(\chi_{6897}(989, \cdot)\)	n/a	7920	10
6897.2.bt	\(\chi_{6897}(977, \cdot)\)	n/a	5632	8
6897.2.bu	\(\chi_{6897}(239, \cdot)\)	n/a	5632	8
6897.2.bv	\(\chi_{6897}(844, \cdot)\)	n/a	2880	8
6897.2.bw	\(\chi_{6897}(463, \cdot)\)	n/a	8800	20
6897.2.bx	\(\chi_{6897}(130, \cdot)\)	n/a	8640	24
6897.2.by	\(\chi_{6897}(58, \cdot)\)	n/a	15840	40
6897.2.cd	\(\chi_{6897}(221, \cdot)\)	n/a	17520	20
6897.2.ce	\(\chi_{6897}(197, \cdot)\)	n/a	17520	20
6897.2.cf	\(\chi_{6897}(274, \cdot)\)	n/a	8800	20
6897.2.ci	\(\chi_{6897}(40, \cdot)\)	n/a	8640	24
6897.2.cj	\(\chi_{6897}(161, \cdot)\)	n/a	16896	24
6897.2.cm	\(\chi_{6897}(269, \cdot)\)	n/a	16896	24
6897.2.cn	\(\chi_{6897}(100, \cdot)\)	n/a	26400	60
6897.2.cs	\(\chi_{6897}(134, \cdot)\)	n/a	31680	40
6897.2.ct	\(\chi_{6897}(113, \cdot)\)	n/a	35040	40
6897.2.cu	\(\chi_{6897}(151, \cdot)\)	n/a	17600	40
6897.2.cv	\(\chi_{6897}(49, \cdot)\)	n/a	35200	80
6897.2.cy	\(\chi_{6897}(10, \cdot)\)	n/a	26400	60
6897.2.cz	\(\chi_{6897}(131, \cdot)\)	n/a	52560	60
6897.2.dc	\(\chi_{6897}(89, \cdot)\)	n/a	52560	60
6897.2.dd	\(\chi_{6897}(46, \cdot)\)	n/a	35200	80
6897.2.de	\(\chi_{6897}(68, \cdot)\)	n/a	70080	80
6897.2.df	\(\chi_{6897}(179, \cdot)\)	n/a	70080	80
6897.2.dk	\(\chi_{6897}(4, \cdot)\)	n/a	105600	240
6897.2.dl	\(\chi_{6897}(14, \cdot)\)	n/a	210240	240
6897.2.do	\(\chi_{6897}(17, \cdot)\)	n/a	210240	240
6897.2.dp	\(\chi_{6897}(13, \cdot)\)	n/a	105600	240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6897))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6897)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2299))\)\(^{\oplus 2}\)