Space of modular forms of level 6050 and weight 2

• Label: 6050.2
• Level: 6050
• Weight: 2
• Dimension: 329059
• Nonzero newspaces: 42
• Sturm bound: 4356000

Defining parameters

Level:	\( N \)	=	\( 6050 = 2 \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(4356000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6050))\).

	Total	New	Old
Modular forms	1097960	329059	768901
Cusp forms	1080041	329059	750982
Eisenstein series	17919	0	17919

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6050))\)

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
6050.2.a	\(\chi_{6050}(1, \cdot)\)	6050.2.a.a	1	1
		6050.2.a.b	1
		6050.2.a.c	1
		6050.2.a.d	1
		6050.2.a.e	1
		6050.2.a.f	1
		6050.2.a.g	1
		6050.2.a.h	1
		6050.2.a.i	1
		6050.2.a.j	1
		6050.2.a.k	1
		6050.2.a.l	1
		6050.2.a.m	1
		6050.2.a.n	1
		6050.2.a.o	1
		6050.2.a.p	1
		6050.2.a.q	1
		6050.2.a.r	1
		6050.2.a.s	1
		6050.2.a.t	1
		6050.2.a.u	1
		6050.2.a.v	1
		6050.2.a.w	1
		6050.2.a.x	1
		6050.2.a.y	1
		6050.2.a.z	1
		6050.2.a.ba	1
		6050.2.a.bb	1
		6050.2.a.bc	1
		6050.2.a.bd	1
		6050.2.a.be	1
		6050.2.a.bf	1
		6050.2.a.bg	1
		6050.2.a.bh	1
		6050.2.a.bi	1
		6050.2.a.bj	1
		6050.2.a.bk	1
		6050.2.a.bl	1
		6050.2.a.bm	1
		6050.2.a.bn	1
		6050.2.a.bo	1
		6050.2.a.bp	1
		6050.2.a.bq	1
		6050.2.a.br	2
		6050.2.a.bs	2
		6050.2.a.bt	2
		6050.2.a.bu	2
		6050.2.a.bv	2
		6050.2.a.bw	2
		6050.2.a.bx	2
		6050.2.a.by	2
		6050.2.a.bz	2
		6050.2.a.ca	2
		6050.2.a.cb	2
		6050.2.a.cc	2
		6050.2.a.cd	2
		6050.2.a.ce	2
		6050.2.a.cf	2
		6050.2.a.cg	2
		6050.2.a.ch	2
		6050.2.a.ci	2
		6050.2.a.cj	2
		6050.2.a.ck	2
		6050.2.a.cl	2
6050.2.a.cm	2
6050.2.a.cn	2
6050.2.a.co	2
6050.2.a.cp	2
6050.2.a.cq	2
6050.2.a.cr	2
6050.2.a.cs	2
6050.2.a.ct	2
6050.2.a.cu	2
6050.2.a.cv	2
6050.2.a.cw	2
6050.2.a.cx	2
6050.2.a.cy	4
6050.2.a.cz	4
6050.2.a.da	4
6050.2.a.db	4
6050.2.a.dc	4
6050.2.a.dd	4
6050.2.a.de	4
6050.2.a.df	4
6050.2.a.dg	4
6050.2.a.dh	4
6050.2.a.di	4
6050.2.a.dj	4
6050.2.a.dk	4
6050.2.a.dl	4
6050.2.a.dm	4
6050.2.a.dn	4
6050.2.b	\(\chi_{6050}(4599, \cdot)\)	n/a	164	1
6050.2.f	\(\chi_{6050}(1693, \cdot)\)	n/a	324	2
6050.2.g	\(\chi_{6050}(1461, \cdot)\)	n/a	1080	4
6050.2.h	\(\chi_{6050}(251, \cdot)\)	n/a	684	4
6050.2.i	\(\chi_{6050}(1721, \cdot)\)	n/a	1080	4
6050.2.j	\(\chi_{6050}(81, \cdot)\)	n/a	1080	4
6050.2.k	\(\chi_{6050}(1211, \cdot)\)	n/a	1092	4
6050.2.l	\(\chi_{6050}(1291, \cdot)\)	n/a	1080	4
6050.2.n	\(\chi_{6050}(269, \cdot)\)	n/a	1080	4
6050.2.t	\(\chi_{6050}(969, \cdot)\)	n/a	1088	4
6050.2.y	\(\chi_{6050}(9, \cdot)\)	n/a	1080	4
6050.2.z	\(\chi_{6050}(3639, \cdot)\)	n/a	1080	4
6050.2.ba	\(\chi_{6050}(1049, \cdot)\)	n/a	648	4
6050.2.bb	\(\chi_{6050}(1219, \cdot)\)	n/a	1080	4
6050.2.be	\(\chi_{6050}(551, \cdot)\)	n/a	2090	10
6050.2.bf	\(\chi_{6050}(723, \cdot)\)	n/a	2160	8
6050.2.bi	\(\chi_{6050}(457, \cdot)\)	n/a	1296	8
6050.2.bj	\(\chi_{6050}(483, \cdot)\)	n/a	2160	8
6050.2.bk	\(\chi_{6050}(2877, \cdot)\)	n/a	2160	8
6050.2.bl	\(\chi_{6050}(403, \cdot)\)	n/a	2160	8
6050.2.bq	\(\chi_{6050}(233, \cdot)\)	n/a	2160	8
6050.2.bs	\(\chi_{6050}(199, \cdot)\)	n/a	1980	10
6050.2.bu	\(\chi_{6050}(43, \cdot)\)	n/a	3960	20
6050.2.bw	\(\chi_{6050}(111, \cdot)\)	n/a	13200	40
6050.2.bx	\(\chi_{6050}(141, \cdot)\)	n/a	13200	40
6050.2.by	\(\chi_{6050}(31, \cdot)\)	n/a	13200	40
6050.2.bz	\(\chi_{6050}(201, \cdot)\)	n/a	8360	40
6050.2.ca	\(\chi_{6050}(291, \cdot)\)	n/a	13200	40
6050.2.cb	\(\chi_{6050}(181, \cdot)\)	n/a	13200	40
6050.2.cc	\(\chi_{6050}(59, \cdot)\)	n/a	13200	40
6050.2.ck	\(\chi_{6050}(119, \cdot)\)	n/a	13200	40
6050.2.cl	\(\chi_{6050}(49, \cdot)\)	n/a	7920	40
6050.2.cm	\(\chi_{6050}(69, \cdot)\)	n/a	13200	40
6050.2.cn	\(\chi_{6050}(169, \cdot)\)	n/a	13200	40
6050.2.cs	\(\chi_{6050}(89, \cdot)\)	n/a	13200	40
6050.2.cv	\(\chi_{6050}(17, \cdot)\)	n/a	26400	80
6050.2.cw	\(\chi_{6050}(63, \cdot)\)	n/a	26400	80
6050.2.db	\(\chi_{6050}(123, \cdot)\)	n/a	26400	80
6050.2.dc	\(\chi_{6050}(13, \cdot)\)	n/a	26400	80
6050.2.dd	\(\chi_{6050}(87, \cdot)\)	n/a	26400	80
6050.2.de	\(\chi_{6050}(7, \cdot)\)	n/a	15840	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6050))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6050)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3025))\)\(^{\oplus 2}\)