Space of modular forms of level 7200 and weight 2

• Label: 7200.2
• Level: 7200
• Weight: 2
• Dimension: 565533
• Nonzero newspaces: 80
• Sturm bound: 5529600

Defining parameters

Level:	\( N \)	=	\( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 80 \)
Sturm bound:			\(5529600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7200))\).

	Total	New	Old
Modular forms	1396736	569223	827513
Cusp forms	1368065	565533	802532
Eisenstein series	28671	3690	24981

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7200))\)

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
7200.2.a	\(\chi_{7200}(1, \cdot)\)	7200.2.a.a	1	1
		7200.2.a.b	1
		7200.2.a.c	1
		7200.2.a.d	1
		7200.2.a.e	1
		7200.2.a.f	1
		7200.2.a.g	1
		7200.2.a.h	1
		7200.2.a.i	1
		7200.2.a.j	1
		7200.2.a.k	1
		7200.2.a.l	1
		7200.2.a.m	1
		7200.2.a.n	1
		7200.2.a.o	1
		7200.2.a.p	1
		7200.2.a.q	1
		7200.2.a.r	1
		7200.2.a.s	1
		7200.2.a.t	1
		7200.2.a.u	1
		7200.2.a.v	1
		7200.2.a.w	1
		7200.2.a.x	1
		7200.2.a.y	1
		7200.2.a.z	1
		7200.2.a.ba	1
		7200.2.a.bb	1
		7200.2.a.bc	1
		7200.2.a.bd	1
		7200.2.a.be	1
		7200.2.a.bf	1
		7200.2.a.bg	1
		7200.2.a.bh	1
		7200.2.a.bi	1
		7200.2.a.bj	1
		7200.2.a.bk	1
		7200.2.a.bl	1
		7200.2.a.bm	1
		7200.2.a.bn	1
		7200.2.a.bo	1
		7200.2.a.bp	1
		7200.2.a.bq	1
		7200.2.a.br	1
		7200.2.a.bs	1
		7200.2.a.bt	1
		7200.2.a.bu	1
		7200.2.a.bv	1
		7200.2.a.bw	1
		7200.2.a.bx	1
		7200.2.a.by	1
		7200.2.a.bz	1
		7200.2.a.ca	1
		7200.2.a.cb	2
		7200.2.a.cc	2
		7200.2.a.cd	2
		7200.2.a.ce	2
		7200.2.a.cf	2
		7200.2.a.cg	2
		7200.2.a.ch	2
		7200.2.a.ci	2
		7200.2.a.cj	2
		7200.2.a.ck	2
		7200.2.a.cl	2
7200.2.a.cm	2
7200.2.a.cn	2
7200.2.a.co	2
7200.2.a.cp	2
7200.2.a.cq	2
7200.2.a.cr	2
7200.2.a.cs	4
7200.2.a.ct	4
7200.2.b	\(\chi_{7200}(4751, \cdot)\)	7200.2.b.a	2	1
		7200.2.b.b	2
		7200.2.b.c	4
		7200.2.b.d	6
		7200.2.b.e	6
		7200.2.b.f	8
		7200.2.b.g	16
		7200.2.b.h	16
		7200.2.b.i	16
7200.2.d	\(\chi_{7200}(2449, \cdot)\)	7200.2.d.a	2	1
		7200.2.d.b	2
		7200.2.d.c	2
		7200.2.d.d	2
		7200.2.d.e	2
		7200.2.d.f	2
		7200.2.d.g	2
		7200.2.d.h	2
		7200.2.d.i	2
		7200.2.d.j	2
		7200.2.d.k	4
		7200.2.d.l	4
		7200.2.d.m	4
		7200.2.d.n	4
		7200.2.d.o	4
		7200.2.d.p	4
		7200.2.d.q	6
		7200.2.d.r	6
		7200.2.d.s	8
		7200.2.d.t	8
		7200.2.d.u	16
7200.2.f	\(\chi_{7200}(6049, \cdot)\)	7200.2.f.a	2	1
		7200.2.f.b	2
		7200.2.f.c	2
		7200.2.f.d	2
		7200.2.f.e	2
		7200.2.f.f	2
		7200.2.f.g	2
		7200.2.f.h	2
		7200.2.f.i	2
		7200.2.f.j	2
		7200.2.f.k	2
		7200.2.f.l	2
		7200.2.f.m	2
		7200.2.f.n	2
		7200.2.f.o	2
		7200.2.f.p	2
		7200.2.f.q	2
		7200.2.f.r	2
		7200.2.f.s	2
		7200.2.f.t	2
		7200.2.f.u	2
		7200.2.f.v	2
		7200.2.f.w	2
		7200.2.f.x	2
		7200.2.f.y	2
		7200.2.f.z	2
		7200.2.f.ba	2
		7200.2.f.bb	2
		7200.2.f.bc	2
		7200.2.f.bd	4
		7200.2.f.be	4
		7200.2.f.bf	4
		7200.2.f.bg	4
		7200.2.f.bh	4
		7200.2.f.bi	4
		7200.2.f.bj	4
		7200.2.f.bk	4
7200.2.h	\(\chi_{7200}(1151, \cdot)\)	7200.2.h.a	4	1
		7200.2.h.b	4
		7200.2.h.c	4
		7200.2.h.d	4
		7200.2.h.e	4
		7200.2.h.f	4
		7200.2.h.g	4
		7200.2.h.h	4
		7200.2.h.i	4
		7200.2.h.j	8
		7200.2.h.k	8
		7200.2.h.l	12
		7200.2.h.m	12
7200.2.k	\(\chi_{7200}(3601, \cdot)\)	7200.2.k.a	2	1
		7200.2.k.b	2
		7200.2.k.c	2
		7200.2.k.d	2
		7200.2.k.e	2
		7200.2.k.f	2
		7200.2.k.g	2
		7200.2.k.h	2
		7200.2.k.i	2
		7200.2.k.j	4
		7200.2.k.k	4
		7200.2.k.l	4
		7200.2.k.m	4
		7200.2.k.n	4
		7200.2.k.o	4
		7200.2.k.p	6
		7200.2.k.q	8
		7200.2.k.r	8
		7200.2.k.s	8
		7200.2.k.t	8
		7200.2.k.u	12
7200.2.m	\(\chi_{7200}(3599, \cdot)\)	7200.2.m.a	4	1
		7200.2.m.b	4
		7200.2.m.c	8
		7200.2.m.d	12
		7200.2.m.e	12
		7200.2.m.f	32
7200.2.o	\(\chi_{7200}(7199, \cdot)\)	7200.2.o.a	4	1
		7200.2.o.b	4
		7200.2.o.c	4
		7200.2.o.d	4
		7200.2.o.e	4
		7200.2.o.f	4
		7200.2.o.g	4
		7200.2.o.h	4
		7200.2.o.i	4
		7200.2.o.j	4
		7200.2.o.k	4
		7200.2.o.l	4
		7200.2.o.m	4
		7200.2.o.n	4
		7200.2.o.o	8
		7200.2.o.p	8
7200.2.q	\(\chi_{7200}(2401, \cdot)\)	n/a	456	2
7200.2.t	\(\chi_{7200}(1801, \cdot)\)	None	0	2
7200.2.u	\(\chi_{7200}(1799, \cdot)\)	None	0	2
7200.2.w	\(\chi_{7200}(4193, \cdot)\)	n/a	144	2
7200.2.x	\(\chi_{7200}(2143, \cdot)\)	n/a	180	2
7200.2.z	\(\chi_{7200}(343, \cdot)\)	None	0	2
7200.2.bc	\(\chi_{7200}(3257, \cdot)\)	None	0	2
7200.2.bd	\(\chi_{7200}(1207, \cdot)\)	None	0	2
7200.2.bg	\(\chi_{7200}(2393, \cdot)\)	None	0	2
7200.2.bi	\(\chi_{7200}(5743, \cdot)\)	n/a	176	2
7200.2.bj	\(\chi_{7200}(593, \cdot)\)	n/a	144	2
7200.2.bl	\(\chi_{7200}(2951, \cdot)\)	None	0	2
7200.2.bm	\(\chi_{7200}(649, \cdot)\)	None	0	2
7200.2.bp	\(\chi_{7200}(1441, \cdot)\)	n/a	600	4
7200.2.bs	\(\chi_{7200}(2399, \cdot)\)	n/a	432	2
7200.2.bu	\(\chi_{7200}(1199, \cdot)\)	n/a	424	2
7200.2.bw	\(\chi_{7200}(1201, \cdot)\)	n/a	444	2
7200.2.bx	\(\chi_{7200}(3551, \cdot)\)	n/a	456	2
7200.2.bz	\(\chi_{7200}(1249, \cdot)\)	n/a	432	2
7200.2.cb	\(\chi_{7200}(49, \cdot)\)	n/a	424	2
7200.2.cd	\(\chi_{7200}(2351, \cdot)\)	n/a	444	2
7200.2.cf	\(\chi_{7200}(307, \cdot)\)	n/a	1432	4
7200.2.ci	\(\chi_{7200}(2357, \cdot)\)	n/a	1152	4
7200.2.cj	\(\chi_{7200}(899, \cdot)\)	n/a	1152	4
7200.2.cm	\(\chi_{7200}(901, \cdot)\)	n/a	1508	4
7200.2.co	\(\chi_{7200}(251, \cdot)\)	n/a	1216	4
7200.2.cp	\(\chi_{7200}(1549, \cdot)\)	n/a	1432	4
7200.2.cs	\(\chi_{7200}(557, \cdot)\)	n/a	1152	4
7200.2.ct	\(\chi_{7200}(2107, \cdot)\)	n/a	1432	4
7200.2.cw	\(\chi_{7200}(2591, \cdot)\)	n/a	480	4
7200.2.cy	\(\chi_{7200}(289, \cdot)\)	n/a	600	4
7200.2.da	\(\chi_{7200}(1009, \cdot)\)	n/a	592	4
7200.2.dc	\(\chi_{7200}(431, \cdot)\)	n/a	480	4
7200.2.de	\(\chi_{7200}(1439, \cdot)\)	n/a	480	4
7200.2.dg	\(\chi_{7200}(719, \cdot)\)	n/a	480	4
7200.2.di	\(\chi_{7200}(721, \cdot)\)	n/a	592	4
7200.2.dk	\(\chi_{7200}(1849, \cdot)\)	None	0	4
7200.2.dl	\(\chi_{7200}(551, \cdot)\)	None	0	4
7200.2.do	\(\chi_{7200}(943, \cdot)\)	n/a	848	4
7200.2.dr	\(\chi_{7200}(2993, \cdot)\)	n/a	848	4
7200.2.ds	\(\chi_{7200}(2057, \cdot)\)	None	0	4
7200.2.dv	\(\chi_{7200}(1543, \cdot)\)	None	0	4
7200.2.dw	\(\chi_{7200}(857, \cdot)\)	None	0	4
7200.2.dz	\(\chi_{7200}(7, \cdot)\)	None	0	4
7200.2.ea	\(\chi_{7200}(257, \cdot)\)	n/a	864	4
7200.2.ed	\(\chi_{7200}(607, \cdot)\)	n/a	864	4
7200.2.eg	\(\chi_{7200}(599, \cdot)\)	None	0	4
7200.2.eh	\(\chi_{7200}(601, \cdot)\)	None	0	4
7200.2.ei	\(\chi_{7200}(481, \cdot)\)	n/a	2880	8
7200.2.ej	\(\chi_{7200}(359, \cdot)\)	None	0	8
7200.2.ek	\(\chi_{7200}(361, \cdot)\)	None	0	8
7200.2.eo	\(\chi_{7200}(17, \cdot)\)	n/a	960	8
7200.2.ep	\(\chi_{7200}(847, \cdot)\)	n/a	1184	8
7200.2.er	\(\chi_{7200}(953, \cdot)\)	None	0	8
7200.2.eu	\(\chi_{7200}(1063, \cdot)\)	None	0	8
7200.2.ev	\(\chi_{7200}(233, \cdot)\)	None	0	8
7200.2.ey	\(\chi_{7200}(487, \cdot)\)	None	0	8
7200.2.fa	\(\chi_{7200}(127, \cdot)\)	n/a	1200	8
7200.2.fb	\(\chi_{7200}(737, \cdot)\)	n/a	960	8
7200.2.ff	\(\chi_{7200}(1369, \cdot)\)	None	0	8
7200.2.fg	\(\chi_{7200}(71, \cdot)\)	None	0	8
7200.2.fi	\(\chi_{7200}(643, \cdot)\)	n/a	6880	8
7200.2.fj	\(\chi_{7200}(293, \cdot)\)	n/a	6880	8
7200.2.fl	\(\chi_{7200}(301, \cdot)\)	n/a	7248	8
7200.2.fo	\(\chi_{7200}(299, \cdot)\)	n/a	6880	8
7200.2.fq	\(\chi_{7200}(349, \cdot)\)	n/a	6880	8
7200.2.fr	\(\chi_{7200}(851, \cdot)\)	n/a	7248	8
7200.2.ft	\(\chi_{7200}(893, \cdot)\)	n/a	6880	8
7200.2.fw	\(\chi_{7200}(43, \cdot)\)	n/a	6880	8
7200.2.fx	\(\chi_{7200}(241, \cdot)\)	n/a	2848	8
7200.2.fz	\(\chi_{7200}(239, \cdot)\)	n/a	2848	8
7200.2.gb	\(\chi_{7200}(479, \cdot)\)	n/a	2880	8
7200.2.gf	\(\chi_{7200}(911, \cdot)\)	n/a	2848	8
7200.2.gh	\(\chi_{7200}(529, \cdot)\)	n/a	2848	8
7200.2.gj	\(\chi_{7200}(769, \cdot)\)	n/a	2880	8
7200.2.gl	\(\chi_{7200}(191, \cdot)\)	n/a	2880	8
7200.2.gm	\(\chi_{7200}(197, \cdot)\)	n/a	7680	16
7200.2.gp	\(\chi_{7200}(523, \cdot)\)	n/a	9568	16
7200.2.gr	\(\chi_{7200}(109, \cdot)\)	n/a	9568	16
7200.2.gs	\(\chi_{7200}(611, \cdot)\)	n/a	7680	16
7200.2.gu	\(\chi_{7200}(181, \cdot)\)	n/a	9568	16
7200.2.gx	\(\chi_{7200}(179, \cdot)\)	n/a	7680	16
7200.2.gz	\(\chi_{7200}(163, \cdot)\)	n/a	9568	16
7200.2.ha	\(\chi_{7200}(53, \cdot)\)	n/a	7680	16
7200.2.he	\(\chi_{7200}(311, \cdot)\)	None	0	16
7200.2.hf	\(\chi_{7200}(169, \cdot)\)	None	0	16
7200.2.hg	\(\chi_{7200}(223, \cdot)\)	n/a	5760	16
7200.2.hj	\(\chi_{7200}(353, \cdot)\)	n/a	5760	16
7200.2.hk	\(\chi_{7200}(823, \cdot)\)	None	0	16
7200.2.hn	\(\chi_{7200}(713, \cdot)\)	None	0	16
7200.2.ho	\(\chi_{7200}(103, \cdot)\)	None	0	16
7200.2.hr	\(\chi_{7200}(137, \cdot)\)	None	0	16
7200.2.hs	\(\chi_{7200}(113, \cdot)\)	n/a	5696	16
7200.2.hv	\(\chi_{7200}(367, \cdot)\)	n/a	5696	16
7200.2.hw	\(\chi_{7200}(121, \cdot)\)	None	0	16
7200.2.hx	\(\chi_{7200}(119, \cdot)\)	None	0	16
7200.2.ib	\(\chi_{7200}(77, \cdot)\)	n/a	45952	32
7200.2.ic	\(\chi_{7200}(187, \cdot)\)	n/a	45952	32
7200.2.if	\(\chi_{7200}(11, \cdot)\)	n/a	45952	32
7200.2.ig	\(\chi_{7200}(229, \cdot)\)	n/a	45952	32
7200.2.ii	\(\chi_{7200}(59, \cdot)\)	n/a	45952	32
7200.2.il	\(\chi_{7200}(61, \cdot)\)	n/a	45952	32
7200.2.im	\(\chi_{7200}(67, \cdot)\)	n/a	45952	32
7200.2.ip	\(\chi_{7200}(173, \cdot)\)	n/a	45952	32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 54}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 45}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3600))\)\(^{\oplus 2}\)