Space of modular forms of level 7581 and weight 2

• Label: 7581.2
• Level: 7581
• Weight: 2
• Dimension: 1481584
• Nonzero newspaces: 64
• Sturm bound: 8317440

Defining parameters

Level:	\( N \)	=	\( 7581 = 3 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 64 \)
Sturm bound:			\(8317440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7581))\).

	Total	New	Old
Modular forms	2091456	1490956	600500
Cusp forms	2067265	1481584	585681
Eisenstein series	24191	9372	14819

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7581))\)

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
7581.2.a	\(\chi_{7581}(1, \cdot)\)	7581.2.a.a	1	1
		7581.2.a.b	1
		7581.2.a.c	1
		7581.2.a.d	1
		7581.2.a.e	1
		7581.2.a.f	1
		7581.2.a.g	2
		7581.2.a.h	2
		7581.2.a.i	2
		7581.2.a.j	2
		7581.2.a.k	3
		7581.2.a.l	3
		7581.2.a.m	3
		7581.2.a.n	3
		7581.2.a.o	3
		7581.2.a.p	3
		7581.2.a.q	4
		7581.2.a.r	4
		7581.2.a.s	4
		7581.2.a.t	4
		7581.2.a.u	4
		7581.2.a.v	4
		7581.2.a.w	5
		7581.2.a.x	5
		7581.2.a.y	6
		7581.2.a.z	6
		7581.2.a.ba	6
		7581.2.a.bb	6
		7581.2.a.bc	6
		7581.2.a.bd	6
		7581.2.a.be	6
		7581.2.a.bf	6
		7581.2.a.bg	9
		7581.2.a.bh	9
		7581.2.a.bi	12
		7581.2.a.bj	12
		7581.2.a.bk	12
		7581.2.a.bl	12
		7581.2.a.bm	12
		7581.2.a.bn	12
		7581.2.a.bo	12
		7581.2.a.bp	12
		7581.2.a.bq	18
		7581.2.a.br	18
		7581.2.a.bs	18
		7581.2.a.bt	18
		7581.2.a.bu	20
		7581.2.a.bv	20
7581.2.c	\(\chi_{7581}(5053, \cdot)\)	n/a	452	1
7581.2.d	\(\chi_{7581}(3611, \cdot)\)	n/a	876	1
7581.2.f	\(\chi_{7581}(6497, \cdot)\)	n/a	680	1
7581.2.i	\(\chi_{7581}(2956, \cdot)\)	n/a	908	2
7581.2.j	\(\chi_{7581}(2167, \cdot)\)	n/a	910	2
7581.2.k	\(\chi_{7581}(2458, \cdot)\)	n/a	680	2
7581.2.l	\(\chi_{7581}(1873, \cdot)\)	n/a	908	2
7581.2.m	\(\chi_{7581}(3181, \cdot)\)	n/a	908	2
7581.2.p	\(\chi_{7581}(1151, \cdot)\)	n/a	1748	2
7581.2.t	\(\chi_{7581}(4040, \cdot)\)	n/a	1360	2
7581.2.w	\(\chi_{7581}(1082, \cdot)\)	n/a	1748	2
7581.2.x	\(\chi_{7581}(2459, \cdot)\)	n/a	1748	2
7581.2.z	\(\chi_{7581}(3317, \cdot)\)	n/a	1752	2
7581.2.bc	\(\chi_{7581}(362, \cdot)\)	n/a	1750	2
7581.2.bd	\(\chi_{7581}(68, \cdot)\)	n/a	1748	2
7581.2.bg	\(\chi_{7581}(430, \cdot)\)	n/a	908	2
7581.2.bh	\(\chi_{7581}(1804, \cdot)\)	n/a	908	2
7581.2.bk	\(\chi_{7581}(2596, \cdot)\)	n/a	904	2
7581.2.bm	\(\chi_{7581}(1376, \cdot)\)	n/a	1748	2
7581.2.bo	\(\chi_{7581}(967, \cdot)\)	n/a	2040	6
7581.2.bp	\(\chi_{7581}(3133, \cdot)\)	n/a	2718	6
7581.2.bq	\(\chi_{7581}(415, \cdot)\)	n/a	2718	6
7581.2.br	\(\chi_{7581}(1199, \cdot)\)	n/a	5250	6
7581.2.bv	\(\chi_{7581}(116, \cdot)\)	n/a	5250	6
7581.2.bw	\(\chi_{7581}(1751, \cdot)\)	n/a	4080	6
7581.2.cb	\(\chi_{7581}(1328, \cdot)\)	n/a	5250	6
7581.2.cc	\(\chi_{7581}(307, \cdot)\)	n/a	2724	6
7581.2.cd	\(\chi_{7581}(1921, \cdot)\)	n/a	2718	6
7581.2.ci	\(\chi_{7581}(2411, \cdot)\)	n/a	5250	6
7581.2.cj	\(\chi_{7581}(62, \cdot)\)	n/a	5244	6
7581.2.ck	\(\chi_{7581}(262, \cdot)\)	n/a	2718	6
7581.2.cm	\(\chi_{7581}(400, \cdot)\)	n/a	6840	18
7581.2.cp	\(\chi_{7581}(113, \cdot)\)	n/a	13680	18
7581.2.cr	\(\chi_{7581}(20, \cdot)\)	n/a	18144	18
7581.2.cs	\(\chi_{7581}(265, \cdot)\)	n/a	9144	18
7581.2.cu	\(\chi_{7581}(121, \cdot)\)	n/a	18216	36
7581.2.cv	\(\chi_{7581}(64, \cdot)\)	n/a	13680	36
7581.2.cw	\(\chi_{7581}(58, \cdot)\)	n/a	18216	36
7581.2.cx	\(\chi_{7581}(163, \cdot)\)	n/a	18216	36
7581.2.cz	\(\chi_{7581}(107, \cdot)\)	n/a	36360	36
7581.2.db	\(\chi_{7581}(160, \cdot)\)	n/a	18288	36
7581.2.de	\(\chi_{7581}(94, \cdot)\)	n/a	18216	36
7581.2.df	\(\chi_{7581}(31, \cdot)\)	n/a	18216	36
7581.2.di	\(\chi_{7581}(311, \cdot)\)	n/a	36360	36
7581.2.dj	\(\chi_{7581}(248, \cdot)\)	n/a	36360	36
7581.2.dm	\(\chi_{7581}(83, \cdot)\)	n/a	36288	36
7581.2.do	\(\chi_{7581}(65, \cdot)\)	n/a	36360	36
7581.2.dp	\(\chi_{7581}(170, \cdot)\)	n/a	36360	36
7581.2.ds	\(\chi_{7581}(8, \cdot)\)	n/a	27360	36
7581.2.dw	\(\chi_{7581}(26, \cdot)\)	n/a	36360	36
7581.2.dz	\(\chi_{7581}(145, \cdot)\)	n/a	18216	36
7581.2.ea	\(\chi_{7581}(4, \cdot)\)	n/a	54756	108
7581.2.eb	\(\chi_{7581}(130, \cdot)\)	n/a	54756	108
7581.2.ec	\(\chi_{7581}(43, \cdot)\)	n/a	41040	108
7581.2.ee	\(\chi_{7581}(10, \cdot)\)	n/a	54756	108
7581.2.ef	\(\chi_{7581}(104, \cdot)\)	n/a	109080	108
7581.2.eg	\(\chi_{7581}(17, \cdot)\)	n/a	108972	108
7581.2.el	\(\chi_{7581}(52, \cdot)\)	n/a	54756	108
7581.2.em	\(\chi_{7581}(13, \cdot)\)	n/a	54648	108
7581.2.en	\(\chi_{7581}(5, \cdot)\)	n/a	108972	108
7581.2.es	\(\chi_{7581}(29, \cdot)\)	n/a	82080	108
7581.2.et	\(\chi_{7581}(86, \cdot)\)	n/a	108972	108
7581.2.ex	\(\chi_{7581}(2, \cdot)\)	n/a	108972	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7581))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7581)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2527))\)\(^{\oplus 2}\)