Space of modular forms of level 7360 and weight 2

• Label: 7360.2
• Level: 7360
• Weight: 2
• Dimension: 830412
• Nonzero newspaces: 56
• Sturm bound: 6488064

Defining parameters

Level:	$N$	=	$7360 = 2^{6} \cdot 5 \cdot 23$
Weight:	$k$	=	$2$
Nonzero newspaces:			$56$
Sturm bound:			$6488064$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(7360))$.

	Total	New	Old
Modular forms	1634688	835956	798732
Cusp forms	1609345	830412	778933
Eisenstein series	25343	5544	19799

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(7360))$

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
7360.2.a	$\chi_{7360}(1, \cdot)$	7360.2.a.a	1	1
		7360.2.a.b	1
		7360.2.a.c	1
		7360.2.a.d	1
		7360.2.a.e	1
		7360.2.a.f	1
		7360.2.a.g	1
		7360.2.a.h	1
		7360.2.a.i	1
		7360.2.a.j	1
		7360.2.a.k	1
		7360.2.a.l	1
		7360.2.a.m	1
		7360.2.a.n	1
		7360.2.a.o	1
		7360.2.a.p	1
		7360.2.a.q	1
		7360.2.a.r	1
		7360.2.a.s	1
		7360.2.a.t	1
		7360.2.a.u	1
		7360.2.a.v	1
		7360.2.a.w	1
		7360.2.a.x	1
		7360.2.a.y	1
		7360.2.a.z	1
		7360.2.a.ba	1
		7360.2.a.bb	1
		7360.2.a.bc	2
		7360.2.a.bd	2
		7360.2.a.be	2
		7360.2.a.bf	2
		7360.2.a.bg	2
		7360.2.a.bh	2
		7360.2.a.bi	2
		7360.2.a.bj	2
		7360.2.a.bk	2
		7360.2.a.bl	2
		7360.2.a.bm	2
		7360.2.a.bn	2
		7360.2.a.bo	2
		7360.2.a.bp	2
		7360.2.a.bq	2
		7360.2.a.br	2
		7360.2.a.bs	2
		7360.2.a.bt	2
		7360.2.a.bu	2
		7360.2.a.bv	2
		7360.2.a.bw	3
		7360.2.a.bx	3
		7360.2.a.by	3
		7360.2.a.bz	3
		7360.2.a.ca	3
		7360.2.a.cb	3
		7360.2.a.cc	3
		7360.2.a.cd	3
		7360.2.a.ce	3
		7360.2.a.cf	3
		7360.2.a.cg	4
		7360.2.a.ch	4
		7360.2.a.ci	4
		7360.2.a.cj	4
		7360.2.a.ck	5
		7360.2.a.cl	5
7360.2.a.cm	5
7360.2.a.cn	5
7360.2.a.co	5
7360.2.a.cp	5
7360.2.a.cq	5
7360.2.a.cr	5
7360.2.a.cs	5
7360.2.a.ct	5
7360.2.a.cu	6
7360.2.a.cv	6
7360.2.b	$\chi_{7360}(3679, \cdot)$	n/a	288	1
7360.2.e	$\chi_{7360}(5889, \cdot)$	n/a	264	1
7360.2.f	$\chi_{7360}(3681, \cdot)$	n/a	176	1
7360.2.i	$\chi_{7360}(1471, \cdot)$	n/a	192	1
7360.2.j	$\chi_{7360}(2209, \cdot)$	n/a	264	1
7360.2.m	$\chi_{7360}(7359, \cdot)$	n/a	284	1
7360.2.n	$\chi_{7360}(5151, \cdot)$	n/a	192	1
7360.2.r	$\chi_{7360}(6577, \cdot)$	n/a	568	2
7360.2.t	$\chi_{7360}(47, \cdot)$	n/a	528	2
7360.2.u	$\chi_{7360}(3311, \cdot)$	n/a	384	2
7360.2.x	$\chi_{7360}(1841, \cdot)$	n/a	352	2
7360.2.y	$\chi_{7360}(1793, \cdot)$	n/a	568	2
7360.2.ba	$\chi_{7360}(2623, \cdot)$	n/a	528	2
7360.2.bd	$\chi_{7360}(1887, \cdot)$	n/a	528	2
7360.2.bf	$\chi_{7360}(1057, \cdot)$	n/a	576	2
7360.2.bg	$\chi_{7360}(369, \cdot)$	n/a	528	2
7360.2.bj	$\chi_{7360}(1839, \cdot)$	n/a	568	2
7360.2.bk	$\chi_{7360}(3727, \cdot)$	n/a	528	2
7360.2.bm	$\chi_{7360}(2897, \cdot)$	n/a	568	2
7360.2.bp	$\chi_{7360}(1703, \cdot)$	None	0	4
7360.2.br	$\chi_{7360}(137, \cdot)$	None	0	4
7360.2.bs	$\chi_{7360}(919, \cdot)$	None	0	4
7360.2.bu	$\chi_{7360}(921, \cdot)$	None	0	4
7360.2.bx	$\chi_{7360}(551, \cdot)$	None	0	4
7360.2.bz	$\chi_{7360}(1289, \cdot)$	None	0	4
7360.2.ca	$\chi_{7360}(967, \cdot)$	None	0	4
7360.2.cc	$\chi_{7360}(873, \cdot)$	None	0	4
7360.2.ce	$\chi_{7360}(961, \cdot)$	n/a	1920	10
7360.2.cg	$\chi_{7360}(413, \cdot)$	n/a	9184	8
7360.2.ci	$\chi_{7360}(1243, \cdot)$	n/a	8448	8
7360.2.ck	$\chi_{7360}(461, \cdot)$	n/a	5632	8
7360.2.cl	$\chi_{7360}(829, \cdot)$	n/a	8448	8
7360.2.co	$\chi_{7360}(459, \cdot)$	n/a	9184	8
7360.2.cp	$\chi_{7360}(91, \cdot)$	n/a	6144	8
7360.2.cr	$\chi_{7360}(1333, \cdot)$	n/a	9184	8
7360.2.ct	$\chi_{7360}(323, \cdot)$	n/a	8448	8
7360.2.cx	$\chi_{7360}(1631, \cdot)$	n/a	1920	10
7360.2.cy	$\chi_{7360}(319, \cdot)$	n/a	2840	10
7360.2.db	$\chi_{7360}(289, \cdot)$	n/a	2880	10
7360.2.dc	$\chi_{7360}(191, \cdot)$	n/a	1920	10
7360.2.df	$\chi_{7360}(1761, \cdot)$	n/a	1920	10
7360.2.dg	$\chi_{7360}(449, \cdot)$	n/a	2840	10
7360.2.dj	$\chi_{7360}(159, \cdot)$	n/a	2880	10
7360.2.dl	$\chi_{7360}(17, \cdot)$	n/a	5680	20
7360.2.dn	$\chi_{7360}(303, \cdot)$	n/a	5680	20
7360.2.dp	$\chi_{7360}(79, \cdot)$	n/a	5680	20
7360.2.dq	$\chi_{7360}(49, \cdot)$	n/a	5680	20
7360.2.ds	$\chi_{7360}(33, \cdot)$	n/a	5760	20
7360.2.du	$\chi_{7360}(223, \cdot)$	n/a	5760	20
7360.2.dx	$\chi_{7360}(127, \cdot)$	n/a	5680	20
7360.2.dz	$\chi_{7360}(513, \cdot)$	n/a	5680	20
7360.2.eb	$\chi_{7360}(81, \cdot)$	n/a	3840	20
7360.2.ec	$\chi_{7360}(111, \cdot)$	n/a	3840	20
7360.2.ee	$\chi_{7360}(463, \cdot)$	n/a	5680	20
7360.2.eg	$\chi_{7360}(273, \cdot)$	n/a	5680	20
7360.2.ej	$\chi_{7360}(57, \cdot)$	None	0	40
7360.2.el	$\chi_{7360}(167, \cdot)$	None	0	40
7360.2.en	$\chi_{7360}(9, \cdot)$	None	0	40
7360.2.ep	$\chi_{7360}(471, \cdot)$	None	0	40
7360.2.eq	$\chi_{7360}(41, \cdot)$	None	0	40
7360.2.es	$\chi_{7360}(199, \cdot)$	None	0	40
7360.2.eu	$\chi_{7360}(153, \cdot)$	None	0	40
7360.2.ew	$\chi_{7360}(87, \cdot)$	None	0	40
7360.2.ey	$\chi_{7360}(3, \cdot)$	n/a	91840	80
7360.2.fa	$\chi_{7360}(53, \cdot)$	n/a	91840	80
7360.2.fd	$\chi_{7360}(11, \cdot)$	n/a	61440	80
7360.2.fe	$\chi_{7360}(19, \cdot)$	n/a	91840	80
7360.2.fh	$\chi_{7360}(29, \cdot)$	n/a	91840	80
7360.2.fi	$\chi_{7360}(101, \cdot)$	n/a	61440	80
7360.2.fl	$\chi_{7360}(123, \cdot)$	n/a	91840	80
7360.2.fn	$\chi_{7360}(37, \cdot)$	n/a	91840	80

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(7360))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(7360)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 28}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(368))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(736))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(920))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1472))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1840))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3680))$$^{\oplus 2}$