Space of modular forms of level 6040 and weight 2

• Label: 6040.2
• Level: 6040
• Weight: 2
• Dimension: 562462
• Nonzero newspaces: 54
• Sturm bound: 4377600

Defining parameters

Level:	\( N \)	=	\( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 54 \)
Sturm bound:			\(4377600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6040))\).

	Total	New	Old
Modular forms	1101600	566038	535562
Cusp forms	1087201	562462	524739
Eisenstein series	14399	3576	10823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6040))\)

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
6040.2.a	\(\chi_{6040}(1, \cdot)\)	6040.2.a.a	1	1
		6040.2.a.b	1
		6040.2.a.c	1
		6040.2.a.d	1
		6040.2.a.e	1
		6040.2.a.f	1
		6040.2.a.g	1
		6040.2.a.h	1
		6040.2.a.i	1
		6040.2.a.j	1
		6040.2.a.k	2
		6040.2.a.l	9
		6040.2.a.m	12
		6040.2.a.n	13
		6040.2.a.o	15
		6040.2.a.p	19
		6040.2.a.q	23
		6040.2.a.r	23
		6040.2.a.s	24
6040.2.b	\(\chi_{6040}(6039, \cdot)\)	None	0	1
6040.2.d	\(\chi_{6040}(1209, \cdot)\)	n/a	224	1
6040.2.g	\(\chi_{6040}(3021, \cdot)\)	n/a	600	1
6040.2.i	\(\chi_{6040}(1811, \cdot)\)	n/a	608	1
6040.2.j	\(\chi_{6040}(4229, \cdot)\)	n/a	900	1
6040.2.l	\(\chi_{6040}(3019, \cdot)\)	n/a	908	1
6040.2.o	\(\chi_{6040}(4831, \cdot)\)	None	0	1
6040.2.q	\(\chi_{6040}(2081, \cdot)\)	n/a	304	2
6040.2.r	\(\chi_{6040}(2717, \cdot)\)	n/a	1816	2
6040.2.u	\(\chi_{6040}(303, \cdot)\)	None	0	2
6040.2.w	\(\chi_{6040}(907, \cdot)\)	n/a	1800	2
6040.2.x	\(\chi_{6040}(2113, \cdot)\)	n/a	456	2
6040.2.z	\(\chi_{6040}(321, \cdot)\)	n/a	608	4
6040.2.ba	\(\chi_{6040}(1931, \cdot)\)	n/a	1216	2
6040.2.bc	\(\chi_{6040}(2901, \cdot)\)	n/a	1216	2
6040.2.bf	\(\chi_{6040}(1089, \cdot)\)	n/a	456	2
6040.2.bh	\(\chi_{6040}(119, \cdot)\)	None	0	2
6040.2.bj	\(\chi_{6040}(2751, \cdot)\)	None	0	2
6040.2.bm	\(\chi_{6040}(939, \cdot)\)	n/a	1816	2
6040.2.bo	\(\chi_{6040}(269, \cdot)\)	n/a	1816	2
6040.2.bq	\(\chi_{6040}(1351, \cdot)\)	None	0	4
6040.2.bt	\(\chi_{6040}(1899, \cdot)\)	n/a	3632	4
6040.2.bv	\(\chi_{6040}(1669, \cdot)\)	n/a	3632	4
6040.2.bw	\(\chi_{6040}(691, \cdot)\)	n/a	2432	4
6040.2.by	\(\chi_{6040}(461, \cdot)\)	n/a	2432	4
6040.2.cb	\(\chi_{6040}(1529, \cdot)\)	n/a	912	4
6040.2.cd	\(\chi_{6040}(2559, \cdot)\)	None	0	4
6040.2.ce	\(\chi_{6040}(33, \cdot)\)	n/a	912	4
6040.2.ch	\(\chi_{6040}(787, \cdot)\)	n/a	3632	4
6040.2.cj	\(\chi_{6040}(183, \cdot)\)	None	0	4
6040.2.ck	\(\chi_{6040}(637, \cdot)\)	n/a	3632	4
6040.2.cm	\(\chi_{6040}(1361, \cdot)\)	n/a	1216	8
6040.2.co	\(\chi_{6040}(993, \cdot)\)	n/a	1824	8
6040.2.cp	\(\chi_{6040}(763, \cdot)\)	n/a	7264	8
6040.2.cr	\(\chi_{6040}(623, \cdot)\)	None	0	8
6040.2.cu	\(\chi_{6040}(1597, \cdot)\)	n/a	7264	8
6040.2.cv	\(\chi_{6040}(81, \cdot)\)	n/a	3040	20
6040.2.cw	\(\chi_{6040}(189, \cdot)\)	n/a	7264	8
6040.2.cy	\(\chi_{6040}(499, \cdot)\)	n/a	7264	8
6040.2.db	\(\chi_{6040}(751, \cdot)\)	None	0	8
6040.2.dd	\(\chi_{6040}(519, \cdot)\)	None	0	8
6040.2.df	\(\chi_{6040}(529, \cdot)\)	n/a	1824	8
6040.2.di	\(\chi_{6040}(581, \cdot)\)	n/a	4864	8
6040.2.dk	\(\chi_{6040}(451, \cdot)\)	n/a	4864	8
6040.2.dm	\(\chi_{6040}(131, \cdot)\)	n/a	12160	20
6040.2.dp	\(\chi_{6040}(9, \cdot)\)	n/a	4560	20
6040.2.dr	\(\chi_{6040}(179, \cdot)\)	n/a	18160	20
6040.2.dt	\(\chi_{6040}(631, \cdot)\)	None	0	20
6040.2.dv	\(\chi_{6040}(261, \cdot)\)	n/a	12160	20
6040.2.dx	\(\chi_{6040}(29, \cdot)\)	n/a	18160	20
6040.2.dz	\(\chi_{6040}(79, \cdot)\)	None	0	20
6040.2.eb	\(\chi_{6040}(197, \cdot)\)	n/a	14528	16
6040.2.ec	\(\chi_{6040}(167, \cdot)\)	None	0	16
6040.2.ee	\(\chi_{6040}(227, \cdot)\)	n/a	14528	16
6040.2.eh	\(\chi_{6040}(113, \cdot)\)	n/a	3648	16
6040.2.ei	\(\chi_{6040}(121, \cdot)\)	n/a	6080	40
6040.2.el	\(\chi_{6040}(127, \cdot)\)	None	0	40
6040.2.em	\(\chi_{6040}(53, \cdot)\)	n/a	36320	40
6040.2.ep	\(\chi_{6040}(123, \cdot)\)	n/a	36320	40
6040.2.eq	\(\chi_{6040}(57, \cdot)\)	n/a	9120	40
6040.2.er	\(\chi_{6040}(259, \cdot)\)	n/a	36320	40
6040.2.et	\(\chi_{6040}(49, \cdot)\)	n/a	9120	40
6040.2.ew	\(\chi_{6040}(51, \cdot)\)	n/a	24320	40
6040.2.ey	\(\chi_{6040}(199, \cdot)\)	None	0	40
6040.2.fa	\(\chi_{6040}(69, \cdot)\)	n/a	36320	40
6040.2.fc	\(\chi_{6040}(21, \cdot)\)	n/a	24320	40
6040.2.fe	\(\chi_{6040}(71, \cdot)\)	None	0	40
6040.2.fg	\(\chi_{6040}(47, \cdot)\)	None	0	80
6040.2.fh	\(\chi_{6040}(13, \cdot)\)	n/a	72640	80
6040.2.fk	\(\chi_{6040}(43, \cdot)\)	n/a	72640	80
6040.2.fl	\(\chi_{6040}(233, \cdot)\)	n/a	18240	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(755))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1510))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3020))\)\(^{\oplus 2}\)