Space of modular forms of level 6384 and weight 2

• Label: 6384.2
• Level: 6384
• Weight: 2
• Dimension: 443108
• Nonzero newspaces: 128
• Sturm bound: 4423680

Defining parameters

Level:	$N$	=	$6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19$
Weight:	$k$	=	$2$
Nonzero newspaces:			$128$
Sturm bound:			$4423680$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(6384))$.

	Total	New	Old
Modular forms	1118016	446164	671852
Cusp forms	1093825	443108	650717
Eisenstein series	24191	3056	21135

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(6384))$

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
6384.2.a	$\chi_{6384}(1, \cdot)$	6384.2.a.a	1	1
		6384.2.a.b	1
		6384.2.a.c	1
		6384.2.a.d	1
		6384.2.a.e	1
		6384.2.a.f	1
		6384.2.a.g	1
		6384.2.a.h	1
		6384.2.a.i	1
		6384.2.a.j	1
		6384.2.a.k	1
		6384.2.a.l	1
		6384.2.a.m	1
		6384.2.a.n	1
		6384.2.a.o	1
		6384.2.a.p	1
		6384.2.a.q	1
		6384.2.a.r	1
		6384.2.a.s	1
		6384.2.a.t	1
		6384.2.a.u	1
		6384.2.a.v	1
		6384.2.a.w	1
		6384.2.a.x	1
		6384.2.a.y	1
		6384.2.a.z	1
		6384.2.a.ba	1
		6384.2.a.bb	1
		6384.2.a.bc	1
		6384.2.a.bd	1
		6384.2.a.be	1
		6384.2.a.bf	1
		6384.2.a.bg	1
		6384.2.a.bh	2
		6384.2.a.bi	2
		6384.2.a.bj	2
		6384.2.a.bk	2
		6384.2.a.bl	2
		6384.2.a.bm	2
		6384.2.a.bn	2
		6384.2.a.bo	2
		6384.2.a.bp	2
		6384.2.a.bq	2
		6384.2.a.br	2
		6384.2.a.bs	2
		6384.2.a.bt	3
		6384.2.a.bu	3
		6384.2.a.bv	3
		6384.2.a.bw	3
		6384.2.a.bx	3
		6384.2.a.by	4
		6384.2.a.bz	4
		6384.2.a.ca	4
		6384.2.a.cb	4
		6384.2.a.cc	5
		6384.2.a.cd	5
		6384.2.a.ce	5
		6384.2.a.cf	5
6384.2.b	$\chi_{6384}(113, \cdot)$	n/a	240	1
6384.2.c	$\chi_{6384}(6271, \cdot)$	n/a	144	1
6384.2.d	$\chi_{6384}(3191, \cdot)$	None	0	1
6384.2.e	$\chi_{6384}(3193, \cdot)$	None	0	1
6384.2.n	$\chi_{6384}(2927, \cdot)$	n/a	216	1
6384.2.o	$\chi_{6384}(3457, \cdot)$	n/a	160	1
6384.2.p	$\chi_{6384}(4409, \cdot)$	None	0	1
6384.2.q	$\chi_{6384}(1975, \cdot)$	None	0	1
6384.2.r	$\chi_{6384}(6119, \cdot)$	None	0	1
6384.2.s	$\chi_{6384}(265, \cdot)$	None	0	1
6384.2.t	$\chi_{6384}(1217, \cdot)$	n/a	288	1
6384.2.u	$\chi_{6384}(5167, \cdot)$	n/a	120	1
6384.2.bd	$\chi_{6384}(3305, \cdot)$	None	0	1
6384.2.be	$\chi_{6384}(3079, \cdot)$	None	0	1
6384.2.bf	$\chi_{6384}(6383, \cdot)$	n/a	320	1
6384.2.bg	$\chi_{6384}(961, \cdot)$	n/a	320	2
6384.2.bh	$\chi_{6384}(3649, \cdot)$	n/a	288	2
6384.2.bi	$\chi_{6384}(3697, \cdot)$	n/a	240	2
6384.2.bj	$\chi_{6384}(1873, \cdot)$	n/a	320	2
6384.2.bl	$\chi_{6384}(1331, \cdot)$	n/a	1728	2
6384.2.bm	$\chi_{6384}(1861, \cdot)$	n/a	1280	2
6384.2.bo	$\chi_{6384}(1709, \cdot)$	n/a	1920	2
6384.2.br	$\chi_{6384}(1483, \cdot)$	n/a	1152	2
6384.2.bs	$\chi_{6384}(1595, \cdot)$	n/a	2544	2
6384.2.bv	$\chi_{6384}(1597, \cdot)$	n/a	864	2
6384.2.bx	$\chi_{6384}(2813, \cdot)$	n/a	2304	2
6384.2.by	$\chi_{6384}(379, \cdot)$	n/a	960	2
6384.2.ca	$\chi_{6384}(2839, \cdot)$	None	0	2
6384.2.cb	$\chi_{6384}(425, \cdot)$	None	0	2
6384.2.cc	$\chi_{6384}(145, \cdot)$	n/a	320	2
6384.2.cd	$\chi_{6384}(4799, \cdot)$	n/a	640	2
6384.2.cm	$\chi_{6384}(121, \cdot)$	None	0	2
6384.2.cn	$\chi_{6384}(1319, \cdot)$	None	0	2
6384.2.co	$\chi_{6384}(2287, \cdot)$	n/a	320	2
6384.2.cp	$\chi_{6384}(977, \cdot)$	n/a	632	2
6384.2.cu	$\chi_{6384}(881, \cdot)$	n/a	632	2
6384.2.cv	$\chi_{6384}(1471, \cdot)$	n/a	240	2
6384.2.cw	$\chi_{6384}(3431, \cdot)$	None	0	2
6384.2.cx	$\chi_{6384}(601, \cdot)$	None	0	2
6384.2.dc	$\chi_{6384}(3127, \cdot)$	None	0	2
6384.2.dd	$\chi_{6384}(1817, \cdot)$	None	0	2
6384.2.de	$\chi_{6384}(2159, \cdot)$	n/a	640	2
6384.2.dj	$\chi_{6384}(1823, \cdot)$	n/a	640	2
6384.2.dk	$\chi_{6384}(4903, \cdot)$	None	0	2
6384.2.dl	$\chi_{6384}(569, \cdot)$	None	0	2
6384.2.dm	$\chi_{6384}(2431, \cdot)$	n/a	320	2
6384.2.dn	$\chi_{6384}(3041, \cdot)$	n/a	576	2
6384.2.do	$\chi_{6384}(2089, \cdot)$	None	0	2
6384.2.dp	$\chi_{6384}(3383, \cdot)$	None	0	2
6384.2.du	$\chi_{6384}(2425, \cdot)$	None	0	2
6384.2.dv	$\chi_{6384}(695, \cdot)$	None	0	2
6384.2.dw	$\chi_{6384}(3679, \cdot)$	n/a	320	2
6384.2.dx	$\chi_{6384}(1265, \cdot)$	n/a	632	2
6384.2.ec	$\chi_{6384}(335, \cdot)$	n/a	640	2
6384.2.ed	$\chi_{6384}(3641, \cdot)$	None	0	2
6384.2.ee	$\chi_{6384}(391, \cdot)$	None	0	2
6384.2.en	$\chi_{6384}(3527, \cdot)$	None	0	2
6384.2.eo	$\chi_{6384}(505, \cdot)$	None	0	2
6384.2.ep	$\chi_{6384}(449, \cdot)$	n/a	480	2
6384.2.eq	$\chi_{6384}(3583, \cdot)$	n/a	320	2
6384.2.ev	$\chi_{6384}(2497, \cdot)$	n/a	320	2
6384.2.ew	$\chi_{6384}(767, \cdot)$	n/a	640	2
6384.2.ex	$\chi_{6384}(487, \cdot)$	None	0	2
6384.2.ey	$\chi_{6384}(4457, \cdot)$	None	0	2
6384.2.fd	$\chi_{6384}(151, \cdot)$	None	0	2
6384.2.fe	$\chi_{6384}(761, \cdot)$	None	0	2
6384.2.ff	$\chi_{6384}(5281, \cdot)$	n/a	320	2
6384.2.fg	$\chi_{6384}(191, \cdot)$	n/a	576	2
6384.2.fh	$\chi_{6384}(457, \cdot)$	None	0	2
6384.2.fi	$\chi_{6384}(5015, \cdot)$	None	0	2
6384.2.fj	$\chi_{6384}(1711, \cdot)$	n/a	288	2
6384.2.fk	$\chi_{6384}(3761, \cdot)$	n/a	632	2
6384.2.fp	$\chi_{6384}(1375, \cdot)$	n/a	320	2
6384.2.fq	$\chi_{6384}(65, \cdot)$	n/a	632	2
6384.2.fr	$\chi_{6384}(1033, \cdot)$	None	0	2
6384.2.fs	$\chi_{6384}(2231, \cdot)$	None	0	2
6384.2.fx	$\chi_{6384}(1721, \cdot)$	None	0	2
6384.2.fy	$\chi_{6384}(2311, \cdot)$	None	0	2
6384.2.fz	$\chi_{6384}(239, \cdot)$	n/a	480	2
6384.2.ga	$\chi_{6384}(3793, \cdot)$	n/a	320	2
6384.2.gf	$\chi_{6384}(3071, \cdot)$	n/a	640	2
6384.2.gg	$\chi_{6384}(2215, \cdot)$	None	0	2
6384.2.gh	$\chi_{6384}(905, \cdot)$	None	0	2
6384.2.gq	$\chi_{6384}(2767, \cdot)$	n/a	320	2
6384.2.gr	$\chi_{6384}(353, \cdot)$	n/a	632	2
6384.2.gs	$\chi_{6384}(3337, \cdot)$	None	0	2
6384.2.gt	$\chi_{6384}(1607, \cdot)$	None	0	2
6384.2.gu	$\chi_{6384}(1681, \cdot)$	n/a	720	6
6384.2.gv	$\chi_{6384}(289, \cdot)$	n/a	960	6
6384.2.gw	$\chi_{6384}(625, \cdot)$	n/a	960	6
6384.2.gx	$\chi_{6384}(829, \cdot)$	n/a	2560	4
6384.2.ha	$\chi_{6384}(2291, \cdot)$	n/a	5088	4
6384.2.hc	$\chi_{6384}(1531, \cdot)$	n/a	2560	4
6384.2.hd	$\chi_{6384}(221, \cdot)$	n/a	5088	4
6384.2.hg	$\chi_{6384}(1171, \cdot)$	n/a	2560	4
6384.2.hh	$\chi_{6384}(1949, \cdot)$	n/a	5088	4
6384.2.hj	$\chi_{6384}(125, \cdot)$	n/a	5088	4
6384.2.hm	$\chi_{6384}(835, \cdot)$	n/a	2560	4
6384.2.hn	$\chi_{6384}(1445, \cdot)$	n/a	4608	4
6384.2.hq	$\chi_{6384}(715, \cdot)$	n/a	1920	4
6384.2.hr	$\chi_{6384}(277, \cdot)$	n/a	2560	4
6384.2.hu	$\chi_{6384}(1475, \cdot)$	n/a	5088	4
6384.2.hw	$\chi_{6384}(1091, \cdot)$	n/a	5088	4
6384.2.hx	$\chi_{6384}(2053, \cdot)$	n/a	2304	4
6384.2.ia	$\chi_{6384}(227, \cdot)$	n/a	5088	4
6384.2.ib	$\chi_{6384}(1261, \cdot)$	n/a	1920	4
6384.2.id	$\chi_{6384}(619, \cdot)$	n/a	2560	4
6384.2.ig	$\chi_{6384}(2501, \cdot)$	n/a	5088	4
6384.2.ii	$\chi_{6384}(1205, \cdot)$	n/a	3840	4
6384.2.ij	$\chi_{6384}(115, \cdot)$	n/a	2304	4
6384.2.im	$\chi_{6384}(2165, \cdot)$	n/a	5088	4
6384.2.in	$\chi_{6384}(1147, \cdot)$	n/a	2560	4
6384.2.iq	$\chi_{6384}(1741, \cdot)$	n/a	2560	4
6384.2.ir	$\chi_{6384}(11, \cdot)$	n/a	5088	4
6384.2.it	$\chi_{6384}(995, \cdot)$	n/a	3840	4
6384.2.iw	$\chi_{6384}(493, \cdot)$	n/a	2560	4
6384.2.ix	$\chi_{6384}(1787, \cdot)$	n/a	4608	4
6384.2.ja	$\chi_{6384}(1357, \cdot)$	n/a	2560	4
6384.2.jc	$\chi_{6384}(2557, \cdot)$	n/a	2560	4
6384.2.jd	$\chi_{6384}(563, \cdot)$	n/a	5088	4
6384.2.jf	$\chi_{6384}(331, \cdot)$	n/a	2560	4
6384.2.ji	$\chi_{6384}(1109, \cdot)$	n/a	5088	4
6384.2.jj	$\chi_{6384}(271, \cdot)$	n/a	960	6
6384.2.jl	$\chi_{6384}(409, \cdot)$	None	0	6
6384.2.jo	$\chi_{6384}(25, \cdot)$	None	0	6
6384.2.jq	$\chi_{6384}(79, \cdot)$	n/a	960	6
6384.2.jr	$\chi_{6384}(1895, \cdot)$	None	0	6
6384.2.jt	$\chi_{6384}(929, \cdot)$	n/a	1896	6
6384.2.jw	$\chi_{6384}(401, \cdot)$	n/a	1896	6
6384.2.jy	$\chi_{6384}(359, \cdot)$	None	0	6
6384.2.jz	$\chi_{6384}(1871, \cdot)$	n/a	1920	6
6384.2.kb	$\chi_{6384}(1913, \cdot)$	None	0	6
6384.2.ke	$\chi_{6384}(2201, \cdot)$	None	0	6
6384.2.kg	$\chi_{6384}(1055, \cdot)$	n/a	1920	6
6384.2.ki	$\chi_{6384}(55, \cdot)$	None	0	6
6384.2.kk	$\chi_{6384}(97, \cdot)$	n/a	960	6
6384.2.km	$\chi_{6384}(295, \cdot)$	None	0	6
6384.2.kp	$\chi_{6384}(1343, \cdot)$	n/a	1920	6
6384.2.kr	$\chi_{6384}(377, \cdot)$	None	0	6
6384.2.ks	$\chi_{6384}(281, \cdot)$	None	0	6
6384.2.ku	$\chi_{6384}(575, \cdot)$	n/a	1440	6
6384.2.kw	$\chi_{6384}(583, \cdot)$	None	0	6
6384.2.la	$\chi_{6384}(1153, \cdot)$	n/a	960	6
6384.2.lc	$\chi_{6384}(871, \cdot)$	None	0	6
6384.2.ld	$\chi_{6384}(17, \cdot)$	n/a	1896	6
6384.2.lf	$\chi_{6384}(887, \cdot)$	None	0	6
6384.2.li	$\chi_{6384}(23, \cdot)$	None	0	6
6384.2.lk	$\chi_{6384}(641, \cdot)$	n/a	1896	6
6384.2.lm	$\chi_{6384}(169, \cdot)$	None	0	6
6384.2.lo	$\chi_{6384}(127, \cdot)$	n/a	720	6
6384.2.lp	$\chi_{6384}(1567, \cdot)$	n/a	960	6
6384.2.lr	$\chi_{6384}(1609, \cdot)$	None	0	6
6384.2.lu	$\chi_{6384}(1457, \cdot)$	n/a	1440	6
6384.2.lw	$\chi_{6384}(1415, \cdot)$	None	0	6
6384.2.lx	$\chi_{6384}(167, \cdot)$	None	0	6
6384.2.lz	$\chi_{6384}(2897, \cdot)$	n/a	1896	6
6384.2.mb	$\chi_{6384}(1321, \cdot)$	None	0	6
6384.2.md	$\chi_{6384}(1279, \cdot)$	n/a	960	6
6384.2.mg	$\chi_{6384}(751, \cdot)$	n/a	960	6
6384.2.mi	$\chi_{6384}(2137, \cdot)$	None	0	6
6384.2.mk	$\chi_{6384}(1495, \cdot)$	None	0	6
6384.2.mn	$\chi_{6384}(199, \cdot)$	None	0	6
6384.2.mp	$\chi_{6384}(241, \cdot)$	n/a	960	6
6384.2.mq	$\chi_{6384}(2825, \cdot)$	None	0	6
6384.2.ms	$\chi_{6384}(2543, \cdot)$	n/a	1920	6
6384.2.mv	$\chi_{6384}(143, \cdot)$	n/a	1920	6
6384.2.mx	$\chi_{6384}(1529, \cdot)$	None	0	6
6384.2.my	$\chi_{6384}(275, \cdot)$	n/a	15264	12
6384.2.nb	$\chi_{6384}(605, \cdot)$	n/a	15264	12
6384.2.nd	$\chi_{6384}(59, \cdot)$	n/a	15264	12
6384.2.ne	$\chi_{6384}(317, \cdot)$	n/a	15264	12
6384.2.ng	$\chi_{6384}(187, \cdot)$	n/a	7680	12
6384.2.nj	$\chi_{6384}(1213, \cdot)$	n/a	7680	12
6384.2.nk	$\chi_{6384}(85, \cdot)$	n/a	5760	12
6384.2.nn	$\chi_{6384}(139, \cdot)$	n/a	7680	12
6384.2.np	$\chi_{6384}(67, \cdot)$	n/a	7680	12
6384.2.nq	$\chi_{6384}(565, \cdot)$	n/a	7680	12
6384.2.nt	$\chi_{6384}(13, \cdot)$	n/a	7680	12
6384.2.nu	$\chi_{6384}(211, \cdot)$	n/a	5760	12
6384.2.nw	$\chi_{6384}(53, \cdot)$	n/a	15264	12
6384.2.nz	$\chi_{6384}(299, \cdot)$	n/a	15264	12
6384.2.oa	$\chi_{6384}(755, \cdot)$	n/a	15264	12
6384.2.od	$\chi_{6384}(29, \cdot)$	n/a	11520	12
6384.2.of	$\chi_{6384}(5, \cdot)$	n/a	15264	12
6384.2.og	$\chi_{6384}(947, \cdot)$	n/a	15264	12
6384.2.oj	$\chi_{6384}(491, \cdot)$	n/a	11520	12
6384.2.ok	$\chi_{6384}(461, \cdot)$	n/a	15264	12
6384.2.om	$\chi_{6384}(325, \cdot)$	n/a	7680	12
6384.2.op	$\chi_{6384}(907, \cdot)$	n/a	7680	12
6384.2.or	$\chi_{6384}(541, \cdot)$	n/a	7680	12
6384.2.os	$\chi_{6384}(283, \cdot)$	n/a	7680	12

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(6384))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(6384)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 40}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 32}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(399))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(798))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1064))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1596))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2128))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3192))$$^{\oplus 2}$