Space of modular forms of level 4114 and weight 2

• Label: 4114.2
• Level: 4114
• Weight: 2
• Dimension: 170180
• Nonzero newspaces: 20
• Sturm bound: 2090880

Defining parameters

Level:	\( N \)	=	\( 4114 = 2 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(2090880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4114))\).

	Total	New	Old
Modular forms	527840	170180	357660
Cusp forms	517601	170180	347421
Eisenstein series	10239	0	10239

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4114))\)

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
4114.2.a	\(\chi_{4114}(1, \cdot)\)	4114.2.a.a	1	1
		4114.2.a.b	1
		4114.2.a.c	1
		4114.2.a.d	1
		4114.2.a.e	2
		4114.2.a.f	2
		4114.2.a.g	2
		4114.2.a.h	2
		4114.2.a.i	2
		4114.2.a.j	2
		4114.2.a.k	2
		4114.2.a.l	2
		4114.2.a.m	2
		4114.2.a.n	2
		4114.2.a.o	3
		4114.2.a.p	3
		4114.2.a.q	3
		4114.2.a.r	3
		4114.2.a.s	3
		4114.2.a.t	3
		4114.2.a.u	4
		4114.2.a.v	4
		4114.2.a.w	4
		4114.2.a.x	4
		4114.2.a.y	4
		4114.2.a.z	4
		4114.2.a.ba	4
		4114.2.a.bb	4
		4114.2.a.bc	4
		4114.2.a.bd	4
		4114.2.a.be	5
		4114.2.a.bf	5
		4114.2.a.bg	8
		4114.2.a.bh	8
		4114.2.a.bi	8
		4114.2.a.bj	8
		4114.2.a.bk	10
		4114.2.a.bl	10
4114.2.b	\(\chi_{4114}(1937, \cdot)\)	n/a	164	1
4114.2.f	\(\chi_{4114}(727, \cdot)\)	n/a	328	2
4114.2.g	\(\chi_{4114}(511, \cdot)\)	n/a	576	4
4114.2.h	\(\chi_{4114}(485, \cdot)\)	n/a	652	4
4114.2.l	\(\chi_{4114}(1291, \cdot)\)	n/a	648	4
4114.2.m	\(\chi_{4114}(375, \cdot)\)	n/a	1760	10
4114.2.n	\(\chi_{4114}(241, \cdot)\)	n/a	1296	8
4114.2.p	\(\chi_{4114}(81, \cdot)\)	n/a	1296	8
4114.2.s	\(\chi_{4114}(67, \cdot)\)	n/a	1980	10
4114.2.v	\(\chi_{4114}(9, \cdot)\)	n/a	2592	16
4114.2.w	\(\chi_{4114}(89, \cdot)\)	n/a	3960	20
4114.2.y	\(\chi_{4114}(69, \cdot)\)	n/a	7040	40
4114.2.ba	\(\chi_{4114}(215, \cdot)\)	n/a	5184	32
4114.2.bc	\(\chi_{4114}(111, \cdot)\)	n/a	7920	40
4114.2.be	\(\chi_{4114}(135, \cdot)\)	n/a	7920	40
4114.2.bh	\(\chi_{4114}(65, \cdot)\)	n/a	15840	80
4114.2.bj	\(\chi_{4114}(47, \cdot)\)	n/a	15840	80
4114.2.bk	\(\chi_{4114}(15, \cdot)\)	n/a	31680	160
4114.2.bm	\(\chi_{4114}(7, \cdot)\)	n/a	63360	320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4114))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4114)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2057))\)\(^{\oplus 2}\)