Space of modular forms of level 6690 and weight 2

• Label: 6690.2
• Level: 6690
• Weight: 2
• Dimension: 273489
• Nonzero newspaces: 24
• Sturm bound: 4773888

Defining parameters

Level:	\( N \)	=	\( 6690 = 2 \cdot 3 \cdot 5 \cdot 223 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(4773888\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6690))\).

	Total	New	Old
Modular forms	1200576	273489	927087
Cusp forms	1186369	273489	912880
Eisenstein series	14207	0	14207

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6690))\)

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
6690.2.a	\(\chi_{6690}(1, \cdot)\)	6690.2.a.a	1	1
		6690.2.a.b	1
		6690.2.a.c	1
		6690.2.a.d	1
		6690.2.a.e	1
		6690.2.a.f	1
		6690.2.a.g	1
		6690.2.a.h	1
		6690.2.a.i	1
		6690.2.a.j	1
		6690.2.a.k	1
		6690.2.a.l	2
		6690.2.a.m	2
		6690.2.a.n	3
		6690.2.a.o	4
		6690.2.a.p	4
		6690.2.a.q	4
		6690.2.a.r	5
		6690.2.a.s	5
		6690.2.a.t	5
		6690.2.a.u	5
		6690.2.a.v	6
		6690.2.a.w	6
		6690.2.a.x	6
		6690.2.a.y	6
		6690.2.a.z	6
		6690.2.a.ba	8
		6690.2.a.bb	8
		6690.2.a.bc	9
		6690.2.a.bd	9
		6690.2.a.be	10
		6690.2.a.bf	12
		6690.2.a.bg	13
6690.2.d	\(\chi_{6690}(1339, \cdot)\)	n/a	220	1
6690.2.e	\(\chi_{6690}(6689, \cdot)\)	n/a	448	1
6690.2.h	\(\chi_{6690}(5351, \cdot)\)	n/a	296	1
6690.2.i	\(\chi_{6690}(931, \cdot)\)	n/a	296	2
6690.2.j	\(\chi_{6690}(1783, \cdot)\)	n/a	448	2
6690.2.k	\(\chi_{6690}(893, \cdot)\)	n/a	888	2
6690.2.n	\(\chi_{6690}(2269, \cdot)\)	n/a	448	2
6690.2.o	\(\chi_{6690}(2939, \cdot)\)	n/a	896	2
6690.2.r	\(\chi_{6690}(1601, \cdot)\)	n/a	600	2
6690.2.w	\(\chi_{6690}(1823, \cdot)\)	n/a	1792	4
6690.2.x	\(\chi_{6690}(853, \cdot)\)	n/a	896	4
6690.2.y	\(\chi_{6690}(751, \cdot)\)	n/a	5472	36
6690.2.z	\(\chi_{6690}(191, \cdot)\)	n/a	10656	36
6690.2.bc	\(\chi_{6690}(59, \cdot)\)	n/a	16128	36
6690.2.bd	\(\chi_{6690}(49, \cdot)\)	n/a	8064	36
6690.2.bg	\(\chi_{6690}(31, \cdot)\)	n/a	10656	72
6690.2.bj	\(\chi_{6690}(17, \cdot)\)	n/a	32256	72
6690.2.bk	\(\chi_{6690}(13, \cdot)\)	n/a	16128	72
6690.2.bn	\(\chi_{6690}(11, \cdot)\)	n/a	21600	72
6690.2.bq	\(\chi_{6690}(149, \cdot)\)	n/a	32256	72
6690.2.br	\(\chi_{6690}(19, \cdot)\)	n/a	16128	72
6690.2.bs	\(\chi_{6690}(67, \cdot)\)	n/a	32256	144
6690.2.bt	\(\chi_{6690}(47, \cdot)\)	n/a	64512	144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6690))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6690)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3345))\)\(^{\oplus 2}\)