Space of modular forms of level 6300 and weight 2

• Label: 6300.2
• Level: 6300
• Weight: 2
• Dimension: 421060
• Nonzero newspaces: 120
• Sturm bound: 4147200

Defining parameters

Level:	$N$	=	$6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	=	$2$
Nonzero newspaces:			$120$
Sturm bound:			$4147200$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(6300))$.

	Total	New	Old
Modular forms	1050240	424752	625488
Cusp forms	1023361	421060	602301
Eisenstein series	26879	3692	23187

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(6300))$

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
6300.2.a	$\chi_{6300}(1, \cdot)$	6300.2.a.a	1	1
		6300.2.a.b	1
		6300.2.a.c	1
		6300.2.a.d	1
		6300.2.a.e	1
		6300.2.a.f	1
		6300.2.a.g	1
		6300.2.a.h	1
		6300.2.a.i	1
		6300.2.a.j	1
		6300.2.a.k	1
		6300.2.a.l	1
		6300.2.a.m	1
		6300.2.a.n	1
		6300.2.a.o	1
		6300.2.a.p	1
		6300.2.a.q	1
		6300.2.a.r	1
		6300.2.a.s	1
		6300.2.a.t	1
		6300.2.a.u	1
		6300.2.a.v	1
		6300.2.a.w	1
		6300.2.a.x	1
		6300.2.a.y	1
		6300.2.a.z	1
		6300.2.a.ba	1
		6300.2.a.bb	1
		6300.2.a.bc	1
		6300.2.a.bd	1
		6300.2.a.be	1
		6300.2.a.bf	1
		6300.2.a.bg	2
		6300.2.a.bh	2
		6300.2.a.bi	2
		6300.2.a.bj	2
		6300.2.a.bk	4
		6300.2.a.bl	4
6300.2.c	$\chi_{6300}(5851, \cdot)$	n/a	374	1
6300.2.d	$\chi_{6300}(3401, \cdot)$	6300.2.d.a	4	1
		6300.2.d.b	4
		6300.2.d.c	4
		6300.2.d.d	12
		6300.2.d.e	12
		6300.2.d.f	16
6300.2.f	$\chi_{6300}(3149, \cdot)$	6300.2.f.a	8	1
		6300.2.f.b	8
		6300.2.f.c	8
		6300.2.f.d	24
6300.2.i	$\chi_{6300}(5599, \cdot)$	n/a	356	1
6300.2.k	$\chi_{6300}(6049, \cdot)$	6300.2.k.a	2	1
		6300.2.k.b	2
		6300.2.k.c	2
		6300.2.k.d	2
		6300.2.k.e	2
		6300.2.k.f	2
		6300.2.k.g	2
		6300.2.k.h	2
		6300.2.k.i	2
		6300.2.k.j	2
		6300.2.k.k	2
		6300.2.k.l	2
		6300.2.k.m	2
		6300.2.k.n	2
		6300.2.k.o	2
		6300.2.k.p	2
		6300.2.k.q	2
		6300.2.k.r	2
		6300.2.k.s	4
		6300.2.k.t	4
6300.2.l	$\chi_{6300}(3599, \cdot)$	n/a	216	1
6300.2.n	$\chi_{6300}(3851, \cdot)$	n/a	228	1
6300.2.q	$\chi_{6300}(3301, \cdot)$	n/a	304	2
6300.2.r	$\chi_{6300}(2101, \cdot)$	n/a	228	2
6300.2.s	$\chi_{6300}(1801, \cdot)$	n/a	126	2
6300.2.t	$\chi_{6300}(1201, \cdot)$	n/a	304	2
6300.2.v	$\chi_{6300}(1457, \cdot)$	6300.2.v.a	4	2
		6300.2.v.b	4
		6300.2.v.c	4
		6300.2.v.d	4
		6300.2.v.e	12
		6300.2.v.f	12
		6300.2.v.g	16
		6300.2.v.h	16
6300.2.w	$\chi_{6300}(2143, \cdot)$	n/a	540	2
6300.2.z	$\chi_{6300}(1007, \cdot)$	n/a	576	2
6300.2.ba	$\chi_{6300}(1693, \cdot)$	n/a	120	2
6300.2.bc	$\chi_{6300}(1261, \cdot)$	n/a	296	4
6300.2.bd	$\chi_{6300}(1699, \cdot)$	n/a	1712	2
6300.2.bg	$\chi_{6300}(1949, \cdot)$	n/a	288	2
6300.2.bi	$\chi_{6300}(2201, \cdot)$	n/a	304	2
6300.2.bj	$\chi_{6300}(1951, \cdot)$	n/a	1800	2
6300.2.bm	$\chi_{6300}(2699, \cdot)$	n/a	576	2
6300.2.bn	$\chi_{6300}(1549, \cdot)$	n/a	120	2
6300.2.bp	$\chi_{6300}(1751, \cdot)$	n/a	1368	2
6300.2.bt	$\chi_{6300}(3551, \cdot)$	n/a	1800	2
6300.2.bw	$\chi_{6300}(1849, \cdot)$	n/a	216	2
6300.2.by	$\chi_{6300}(3299, \cdot)$	n/a	1712	2
6300.2.bz	$\chi_{6300}(3049, \cdot)$	n/a	288	2
6300.2.cb	$\chi_{6300}(1499, \cdot)$	n/a	1296	2
6300.2.cf	$\chi_{6300}(2951, \cdot)$	n/a	608	2
6300.2.ch	$\chi_{6300}(1601, \cdot)$	6300.2.ch.a	4	2
		6300.2.ch.b	12
		6300.2.ch.c	12
		6300.2.ch.d	20
		6300.2.ch.e	20
		6300.2.ch.f	32
6300.2.ci	$\chi_{6300}(451, \cdot)$	n/a	748	2
6300.2.ck	$\chi_{6300}(1049, \cdot)$	n/a	288	2
6300.2.cm	$\chi_{6300}(4399, \cdot)$	n/a	1712	2
6300.2.cp	$\chi_{6300}(5549, \cdot)$	n/a	288	2
6300.2.cr	$\chi_{6300}(1399, \cdot)$	n/a	1712	2
6300.2.ct	$\chi_{6300}(1651, \cdot)$	n/a	1800	2
6300.2.cv	$\chi_{6300}(101, \cdot)$	n/a	304	2
6300.2.cw	$\chi_{6300}(4651, \cdot)$	n/a	1800	2
6300.2.cy	$\chi_{6300}(1301, \cdot)$	n/a	304	2
6300.2.da	$\chi_{6300}(199, \cdot)$	n/a	712	2
6300.2.dd	$\chi_{6300}(1349, \cdot)$	6300.2.dd.a	8	2
		6300.2.dd.b	24
		6300.2.dd.c	24
		6300.2.dd.d	40
6300.2.dg	$\chi_{6300}(851, \cdot)$	n/a	1800	2
6300.2.di	$\chi_{6300}(599, \cdot)$	n/a	1712	2
6300.2.dj	$\chi_{6300}(949, \cdot)$	n/a	288	2
6300.2.dn	$\chi_{6300}(71, \cdot)$	n/a	1440	4
6300.2.dp	$\chi_{6300}(1079, \cdot)$	n/a	1440	4
6300.2.dq	$\chi_{6300}(1009, \cdot)$	n/a	304	4
6300.2.ds	$\chi_{6300}(559, \cdot)$	n/a	2384	4
6300.2.dv	$\chi_{6300}(629, \cdot)$	n/a	320	4
6300.2.dx	$\chi_{6300}(881, \cdot)$	n/a	320	4
6300.2.dy	$\chi_{6300}(811, \cdot)$	n/a	2384	4
6300.2.eb	$\chi_{6300}(1843, \cdot)$	n/a	3424	4
6300.2.ec	$\chi_{6300}(2993, \cdot)$	n/a	576	4
6300.2.ee	$\chi_{6300}(1343, \cdot)$	n/a	3424	4
6300.2.eg	$\chi_{6300}(1657, \cdot)$	n/a	240	4
6300.2.ei	$\chi_{6300}(493, \cdot)$	n/a	576	4
6300.2.el	$\chi_{6300}(1643, \cdot)$	n/a	3424	4
6300.2.en	$\chi_{6300}(143, \cdot)$	n/a	1152	4
6300.2.ep	$\chi_{6300}(1357, \cdot)$	n/a	576	4
6300.2.eq	$\chi_{6300}(1793, \cdot)$	n/a	432	4
6300.2.es	$\chi_{6300}(1243, \cdot)$	n/a	1424	4
6300.2.eu	$\chi_{6300}(907, \cdot)$	n/a	3424	4
6300.2.ex	$\chi_{6300}(893, \cdot)$	n/a	576	4
6300.2.ez	$\chi_{6300}(557, \cdot)$	n/a	192	4
6300.2.fb	$\chi_{6300}(43, \cdot)$	n/a	2592	4
6300.2.fd	$\chi_{6300}(157, \cdot)$	n/a	576	4
6300.2.fe	$\chi_{6300}(1307, \cdot)$	n/a	3424	4
6300.2.fg	$\chi_{6300}(961, \cdot)$	n/a	1920	8
6300.2.fh	$\chi_{6300}(361, \cdot)$	n/a	800	8
6300.2.fi	$\chi_{6300}(421, \cdot)$	n/a	1440	8
6300.2.fj	$\chi_{6300}(121, \cdot)$	n/a	1920	8
6300.2.fl	$\chi_{6300}(433, \cdot)$	n/a	800	8
6300.2.fm	$\chi_{6300}(503, \cdot)$	n/a	3840	8
6300.2.fp	$\chi_{6300}(127, \cdot)$	n/a	3600	8
6300.2.fq	$\chi_{6300}(197, \cdot)$	n/a	480	8
6300.2.ft	$\chi_{6300}(709, \cdot)$	n/a	1920	8
6300.2.fu	$\chi_{6300}(1859, \cdot)$	n/a	11456	8
6300.2.fw	$\chi_{6300}(191, \cdot)$	n/a	11456	8
6300.2.fz	$\chi_{6300}(89, \cdot)$	n/a	640	8
6300.2.gc	$\chi_{6300}(19, \cdot)$	n/a	4768	8
6300.2.ge	$\chi_{6300}(41, \cdot)$	n/a	1920	8
6300.2.gg	$\chi_{6300}(871, \cdot)$	n/a	11456	8
6300.2.gh	$\chi_{6300}(761, \cdot)$	n/a	1920	8
6300.2.gj	$\chi_{6300}(391, \cdot)$	n/a	11456	8
6300.2.gl	$\chi_{6300}(139, \cdot)$	n/a	11456	8
6300.2.gn	$\chi_{6300}(509, \cdot)$	n/a	1920	8
6300.2.gq	$\chi_{6300}(619, \cdot)$	n/a	11456	8
6300.2.gs	$\chi_{6300}(209, \cdot)$	n/a	1920	8
6300.2.gu	$\chi_{6300}(271, \cdot)$	n/a	4768	8
6300.2.gv	$\chi_{6300}(341, \cdot)$	n/a	640	8
6300.2.gx	$\chi_{6300}(431, \cdot)$	n/a	3840	8
6300.2.hb	$\chi_{6300}(239, \cdot)$	n/a	8640	8
6300.2.hd	$\chi_{6300}(529, \cdot)$	n/a	1920	8
6300.2.he	$\chi_{6300}(779, \cdot)$	n/a	11456	8
6300.2.hg	$\chi_{6300}(169, \cdot)$	n/a	1440	8
6300.2.hj	$\chi_{6300}(11, \cdot)$	n/a	11456	8
6300.2.hn	$\chi_{6300}(491, \cdot)$	n/a	8640	8
6300.2.hp	$\chi_{6300}(109, \cdot)$	n/a	800	8
6300.2.hq	$\chi_{6300}(179, \cdot)$	n/a	3840	8
6300.2.ht	$\chi_{6300}(31, \cdot)$	n/a	11456	8
6300.2.hu	$\chi_{6300}(941, \cdot)$	n/a	1920	8
6300.2.hw	$\chi_{6300}(689, \cdot)$	n/a	1920	8
6300.2.hz	$\chi_{6300}(439, \cdot)$	n/a	11456	8
6300.2.ib	$\chi_{6300}(47, \cdot)$	n/a	22912	16
6300.2.ic	$\chi_{6300}(313, \cdot)$	n/a	3840	16
6300.2.ie	$\chi_{6300}(463, \cdot)$	n/a	17280	16
6300.2.ig	$\chi_{6300}(53, \cdot)$	n/a	1280	16
6300.2.ii	$\chi_{6300}(137, \cdot)$	n/a	3840	16
6300.2.il	$\chi_{6300}(247, \cdot)$	n/a	22912	16
6300.2.in	$\chi_{6300}(163, \cdot)$	n/a	9536	16
6300.2.ip	$\chi_{6300}(113, \cdot)$	n/a	2880	16
6300.2.iq	$\chi_{6300}(13, \cdot)$	n/a	3840	16
6300.2.is	$\chi_{6300}(467, \cdot)$	n/a	7680	16
6300.2.iu	$\chi_{6300}(227, \cdot)$	n/a	22912	16
6300.2.ix	$\chi_{6300}(733, \cdot)$	n/a	3840	16
6300.2.iz	$\chi_{6300}(73, \cdot)$	n/a	1600	16
6300.2.jb	$\chi_{6300}(83, \cdot)$	n/a	22912	16
6300.2.jd	$\chi_{6300}(317, \cdot)$	n/a	3840	16
6300.2.je	$\chi_{6300}(67, \cdot)$	n/a	22912	16

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(6300))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(6300)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 54}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 27}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(350))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(630))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(700))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(900))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1050))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1260))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1575))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2100))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3150))$$^{\oplus 2}$