Space of modular forms of level 4788 and weight 2

• Label: 4788.2
• Level: 4788
• Weight: 2
• Dimension: 272254
• Nonzero newspaces: 184
• Sturm bound: 2488320

Defining parameters

Level:	$N$	=	$4788 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 19$
Weight:	$k$	=	$2$
Nonzero newspaces:			$184$
Sturm bound:			$2488320$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4788))$.

	Total	New	Old
Modular forms	630720	275310	355410
Cusp forms	613441	272254	341187
Eisenstein series	17279	3056	14223

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4788))$

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
4788.2.a	$\chi_{4788}(1, \cdot)$	4788.2.a.a	1	1
		4788.2.a.b	1
		4788.2.a.c	1
		4788.2.a.d	1
		4788.2.a.e	1
		4788.2.a.f	1
		4788.2.a.g	2
		4788.2.a.h	2
		4788.2.a.i	2
		4788.2.a.j	2
		4788.2.a.k	2
		4788.2.a.l	2
		4788.2.a.m	2
		4788.2.a.n	2
		4788.2.a.o	3
		4788.2.a.p	3
		4788.2.a.q	4
		4788.2.a.r	4
		4788.2.a.s	4
		4788.2.a.t	6
4788.2.b	$\chi_{4788}(1709, \cdot)$	4788.2.b.a	2	1
		4788.2.b.b	2
		4788.2.b.c	16
		4788.2.b.d	20
4788.2.c	$\chi_{4788}(3079, \cdot)$	n/a	360	1
4788.2.h	$\chi_{4788}(1331, \cdot)$	n/a	216	1
4788.2.i	$\chi_{4788}(3457, \cdot)$	4788.2.i.a	2	1
		4788.2.i.b	2
		4788.2.i.c	4
		4788.2.i.d	8
		4788.2.i.e	8
		4788.2.i.f	14
		4788.2.i.g	14
		4788.2.i.h	16
4788.2.j	$\chi_{4788}(4409, \cdot)$	4788.2.j.a	48	1
4788.2.k	$\chi_{4788}(379, \cdot)$	n/a	300	1
4788.2.p	$\chi_{4788}(4787, \cdot)$	n/a	320	1
4788.2.q	$\chi_{4788}(3649, \cdot)$	n/a	288	2
4788.2.r	$\chi_{4788}(121, \cdot)$	n/a	320	2
4788.2.s	$\chi_{4788}(1597, \cdot)$	n/a	216	2
4788.2.t	$\chi_{4788}(2557, \cdot)$	n/a	132	2
4788.2.u	$\chi_{4788}(1369, \cdot)$	n/a	120	2
4788.2.v	$\chi_{4788}(2101, \cdot)$	n/a	240	2
4788.2.w	$\chi_{4788}(505, \cdot)$	4788.2.w.a	2	2
		4788.2.w.b	2
		4788.2.w.c	2
		4788.2.w.d	8
		4788.2.w.e	8
		4788.2.w.f	8
		4788.2.w.g	8
		4788.2.w.h	10
		4788.2.w.i	12
		4788.2.w.j	20
		4788.2.w.k	20
4788.2.x	$\chi_{4788}(961, \cdot)$	n/a	320	2
4788.2.y	$\chi_{4788}(1717, \cdot)$	n/a	320	2
4788.2.z	$\chi_{4788}(1873, \cdot)$	n/a	132	2
4788.2.ba	$\chi_{4788}(2857, \cdot)$	n/a	240	2
4788.2.bb	$\chi_{4788}(1033, \cdot)$	n/a	320	2
4788.2.bc	$\chi_{4788}(457, \cdot)$	n/a	288	2
4788.2.bf	$\chi_{4788}(3307, \cdot)$	n/a	1728	2
4788.2.bg	$\chi_{4788}(569, \cdot)$	n/a	320	2
4788.2.bj	$\chi_{4788}(1357, \cdot)$	n/a	320	2
4788.2.bk	$\chi_{4788}(995, \cdot)$	n/a	1440	2
4788.2.bl	$\chi_{4788}(145, \cdot)$	n/a	132	2
4788.2.bm	$\chi_{4788}(3203, \cdot)$	n/a	640	2
4788.2.br	$\chi_{4788}(767, \cdot)$	n/a	1904	2
4788.2.bs	$\chi_{4788}(2497, \cdot)$	n/a	320	2
4788.2.bt	$\chi_{4788}(1661, \cdot)$	n/a	320	2
4788.2.bu	$\chi_{4788}(1375, \cdot)$	n/a	1904	2
4788.2.bz	$\chi_{4788}(2215, \cdot)$	n/a	792	2
4788.2.ca	$\chi_{4788}(2501, \cdot)$	n/a	104	2
4788.2.cb	$\chi_{4788}(1147, \cdot)$	n/a	1904	2
4788.2.cc	$\chi_{4788}(2801, \cdot)$	n/a	240	2
4788.2.cf	$\chi_{4788}(3685, \cdot)$	n/a	320	2
4788.2.cg	$\chi_{4788}(191, \cdot)$	n/a	1728	2
4788.2.cj	$\chi_{4788}(2839, \cdot)$	n/a	1904	2
4788.2.ck	$\chi_{4788}(425, \cdot)$	n/a	320	2
4788.2.cp	$\chi_{4788}(125, \cdot)$	n/a	112	2
4788.2.cq	$\chi_{4788}(3907, \cdot)$	n/a	600	2
4788.2.cr	$\chi_{4788}(331, \cdot)$	n/a	1904	2
4788.2.cs	$\chi_{4788}(2705, \cdot)$	n/a	320	2
4788.2.cz	$\chi_{4788}(227, \cdot)$	n/a	1904	2
4788.2.da	$\chi_{4788}(4511, \cdot)$	n/a	1904	2
4788.2.db	$\chi_{4788}(1595, \cdot)$	n/a	1904	2
4788.2.dc	$\chi_{4788}(2159, \cdot)$	n/a	640	2
4788.2.dl	$\chi_{4788}(2735, \cdot)$	n/a	640	2
4788.2.dm	$\chi_{4788}(335, \cdot)$	n/a	1904	2
4788.2.dn	$\chi_{4788}(1471, \cdot)$	n/a	1440	2
4788.2.do	$\chi_{4788}(2477, \cdot)$	n/a	320	2
4788.2.dp	$\chi_{4788}(1747, \cdot)$	n/a	792	2
4788.2.dq	$\chi_{4788}(2357, \cdot)$	4788.2.dq.a	96	2
4788.2.dz	$\chi_{4788}(353, \cdot)$	n/a	320	2
4788.2.ea	$\chi_{4788}(2767, \cdot)$	n/a	1904	2
4788.2.eb	$\chi_{4788}(761, \cdot)$	n/a	288	2
4788.2.ec	$\chi_{4788}(151, \cdot)$	n/a	1904	2
4788.2.ed	$\chi_{4788}(487, \cdot)$	n/a	792	2
4788.2.ee	$\chi_{4788}(2861, \cdot)$	n/a	104	2
4788.2.ef	$\chi_{4788}(1975, \cdot)$	n/a	1440	2
4788.2.eg	$\chi_{4788}(1217, \cdot)$	n/a	288	2
4788.2.en	$\chi_{4788}(3527, \cdot)$	n/a	640	2
4788.2.eo	$\chi_{4788}(563, \cdot)$	n/a	1904	2
4788.2.et	$\chi_{4788}(1319, \cdot)$	n/a	1904	2
4788.2.eu	$\chi_{4788}(691, \cdot)$	n/a	1904	2
4788.2.ev	$\chi_{4788}(977, \cdot)$	n/a	320	2
4788.2.fa	$\chi_{4788}(4567, \cdot)$	n/a	1904	2
4788.2.fb	$\chi_{4788}(65, \cdot)$	n/a	320	2
4788.2.fc	$\chi_{4788}(449, \cdot)$	4788.2.fc.a	40	2
		4788.2.fc.b	40
4788.2.fd	$\chi_{4788}(3583, \cdot)$	n/a	792	2
4788.2.fk	$\chi_{4788}(265, \cdot)$	n/a	320	2
4788.2.fl	$\chi_{4788}(2927, \cdot)$	n/a	1296	2
4788.2.fm	$\chi_{4788}(829, \cdot)$	n/a	132	2
4788.2.fn	$\chi_{4788}(3887, \cdot)$	n/a	640	2
4788.2.fo	$\chi_{4788}(1787, \cdot)$	n/a	1728	2
4788.2.fp	$\chi_{4788}(493, \cdot)$	n/a	320	2
4788.2.fq	$\chi_{4788}(11, \cdot)$	n/a	1904	2
4788.2.fr	$\chi_{4788}(1741, \cdot)$	n/a	320	2
4788.2.ga	$\chi_{4788}(1405, \cdot)$	n/a	132	2
4788.2.gb	$\chi_{4788}(2699, \cdot)$	n/a	576	2
4788.2.gc	$\chi_{4788}(601, \cdot)$	n/a	320	2
4788.2.gd	$\chi_{4788}(239, \cdot)$	n/a	1440	2
4788.2.ge	$\chi_{4788}(391, \cdot)$	n/a	1904	2
4788.2.gf	$\chi_{4788}(2045, \cdot)$	n/a	240	2
4788.2.gg	$\chi_{4788}(1027, \cdot)$	n/a	720	2
4788.2.gh	$\chi_{4788}(3077, \cdot)$	n/a	104	2
4788.2.gq	$\chi_{4788}(1531, \cdot)$	n/a	792	2
4788.2.gr	$\chi_{4788}(1817, \cdot)$	n/a	104	2
4788.2.gs	$\chi_{4788}(1483, \cdot)$	n/a	1728	2
4788.2.gt	$\chi_{4788}(113, \cdot)$	n/a	240	2
4788.2.gu	$\chi_{4788}(905, \cdot)$	n/a	320	2
4788.2.gv	$\chi_{4788}(619, \cdot)$	n/a	1904	2
4788.2.gw	$\chi_{4788}(2165, \cdot)$	n/a	320	2
4788.2.gx	$\chi_{4788}(115, \cdot)$	n/a	1728	2
4788.2.he	$\chi_{4788}(2425, \cdot)$	n/a	320	2
4788.2.hf	$\chi_{4788}(695, \cdot)$	n/a	1904	2
4788.2.hg	$\chi_{4788}(1835, \cdot)$	n/a	480	2
4788.2.hh	$\chi_{4788}(2197, \cdot)$	n/a	136	2
4788.2.hm	$\chi_{4788}(3181, \cdot)$	n/a	320	2
4788.2.hn	$\chi_{4788}(1451, \cdot)$	n/a	1904	2
4788.2.hq	$\chi_{4788}(835, \cdot)$	n/a	1904	2
4788.2.hr	$\chi_{4788}(1445, \cdot)$	n/a	288	2
4788.2.hu	$\chi_{4788}(1475, \cdot)$	n/a	640	2
4788.2.hv	$\chi_{4788}(1091, \cdot)$	n/a	1904	2
4788.2.ia	$\chi_{4788}(635, \cdot)$	n/a	1904	2
4788.2.ib	$\chi_{4788}(1109, \cdot)$	n/a	320	2
4788.2.ic	$\chi_{4788}(3523, \cdot)$	n/a	1904	2
4788.2.ih	$\chi_{4788}(715, \cdot)$	n/a	1440	2
4788.2.ii	$\chi_{4788}(1721, \cdot)$	n/a	320	2
4788.2.ij	$\chi_{4788}(1171, \cdot)$	n/a	792	2
4788.2.ik	$\chi_{4788}(3545, \cdot)$	n/a	104	2
4788.2.in	$\chi_{4788}(1823, \cdot)$	n/a	1904	2
4788.2.iq	$\chi_{4788}(709, \cdot)$	n/a	960	6
4788.2.ir	$\chi_{4788}(25, \cdot)$	n/a	960	6
4788.2.is	$\chi_{4788}(253, \cdot)$	n/a	300	6
4788.2.it	$\chi_{4788}(85, \cdot)$	n/a	720	6
4788.2.iu	$\chi_{4788}(289, \cdot)$	n/a	402	6
4788.2.iv	$\chi_{4788}(1201, \cdot)$	n/a	960	6
4788.2.iw	$\chi_{4788}(1297, \cdot)$	n/a	402	6
4788.2.ix	$\chi_{4788}(529, \cdot)$	n/a	960	6
4788.2.iy	$\chi_{4788}(841, \cdot)$	n/a	720	6
4788.2.ja	$\chi_{4788}(29, \cdot)$	n/a	720	6
4788.2.jb	$\chi_{4788}(1469, \cdot)$	n/a	960	6
4788.2.jd	$\chi_{4788}(199, \cdot)$	n/a	2376	6
4788.2.je	$\chi_{4788}(859, \cdot)$	n/a	5712	6
4788.2.jj	$\chi_{4788}(751, \cdot)$	n/a	5712	6
4788.2.jk	$\chi_{4788}(667, \cdot)$	n/a	2376	6
4788.2.jn	$\chi_{4788}(1277, \cdot)$	n/a	324	6
4788.2.jo	$\chi_{4788}(605, \cdot)$	n/a	960	6
4788.2.jp	$\chi_{4788}(641, \cdot)$	n/a	960	6
4788.2.jq	$\chi_{4788}(53, \cdot)$	n/a	324	6
4788.2.jt	$\chi_{4788}(211, \cdot)$	n/a	4320	6
4788.2.jw	$\chi_{4788}(643, \cdot)$	n/a	5712	6
4788.2.jx	$\chi_{4788}(1619, \cdot)$	n/a	1920	6
4788.2.jy	$\chi_{4788}(947, \cdot)$	n/a	5712	6
4788.2.kd	$\chi_{4788}(299, \cdot)$	n/a	5712	6
4788.2.ke	$\chi_{4788}(1655, \cdot)$	n/a	1920	6
4788.2.kh	$\chi_{4788}(13, \cdot)$	n/a	960	6
4788.2.ki	$\chi_{4788}(181, \cdot)$	n/a	396	6
4788.2.kn	$\chi_{4788}(1321, \cdot)$	n/a	960	6
4788.2.ko	$\chi_{4788}(241, \cdot)$	n/a	960	6
4788.2.kr	$\chi_{4788}(167, \cdot)$	n/a	5712	6
4788.2.ks	$\chi_{4788}(755, \cdot)$	n/a	1920	6
4788.2.kx	$\chi_{4788}(1031, \cdot)$	n/a	5712	6
4788.2.ky	$\chi_{4788}(347, \cdot)$	n/a	5712	6
4788.2.kz	$\chi_{4788}(383, \cdot)$	n/a	5712	6
4788.2.la	$\chi_{4788}(59, \cdot)$	n/a	5712	6
4788.2.lf	$\chi_{4788}(575, \cdot)$	n/a	1440	6
4788.2.lg	$\chi_{4788}(2171, \cdot)$	n/a	4320	6
4788.2.lj	$\chi_{4788}(409, \cdot)$	n/a	960	6
4788.2.lk	$\chi_{4788}(325, \cdot)$	n/a	402	6
4788.2.ln	$\chi_{4788}(17, \cdot)$	n/a	324	6
4788.2.lo	$\chi_{4788}(929, \cdot)$	n/a	960	6
4788.2.lt	$\chi_{4788}(1229, \cdot)$	n/a	960	6
4788.2.lu	$\chi_{4788}(485, \cdot)$	n/a	324	6
4788.2.lx	$\chi_{4788}(1723, \cdot)$	n/a	4320	6
4788.2.ly	$\chi_{4788}(127, \cdot)$	n/a	1800	6
4788.2.lz	$\chi_{4788}(283, \cdot)$	n/a	5712	6
4788.2.ma	$\chi_{4788}(367, \cdot)$	n/a	5712	6
4788.2.mf	$\chi_{4788}(583, \cdot)$	n/a	5712	6
4788.2.mg	$\chi_{4788}(1663, \cdot)$	n/a	5712	6
4788.2.mh	$\chi_{4788}(55, \cdot)$	n/a	2376	6
4788.2.mi	$\chi_{4788}(139, \cdot)$	n/a	5712	6
4788.2.ml	$\chi_{4788}(1541, \cdot)$	n/a	720	6
4788.2.mm	$\chi_{4788}(953, \cdot)$	n/a	240	6
4788.2.mr	$\chi_{4788}(5, \cdot)$	n/a	960	6
4788.2.ms	$\chi_{4788}(689, \cdot)$	n/a	960	6
4788.2.mt	$\chi_{4788}(401, \cdot)$	n/a	960	6
4788.2.mu	$\chi_{4788}(317, \cdot)$	n/a	960	6
4788.2.mz	$\chi_{4788}(377, \cdot)$	n/a	312	6
4788.2.na	$\chi_{4788}(461, \cdot)$	n/a	960	6
4788.2.nd	$\chi_{4788}(955, \cdot)$	n/a	2376	6
4788.2.ne	$\chi_{4788}(187, \cdot)$	n/a	5712	6
4788.2.nf	$\chi_{4788}(67, \cdot)$	n/a	5712	6
4788.2.ng	$\chi_{4788}(991, \cdot)$	n/a	2376	6
4788.2.nk	$\chi_{4788}(1343, \cdot)$	n/a	5712	6
4788.2.nl	$\chi_{4788}(491, \cdot)$	n/a	4320	6
4788.2.nr	$\chi_{4788}(1249, \cdot)$	n/a	960	6
4788.2.ns	$\chi_{4788}(649, \cdot)$	n/a	402	6
4788.2.nv	$\chi_{4788}(359, \cdot)$	n/a	1920	6
4788.2.nw	$\chi_{4788}(23, \cdot)$	n/a	5712	6
4788.2.nx	$\chi_{4788}(887, \cdot)$	n/a	5712	6
4788.2.ny	$\chi_{4788}(143, \cdot)$	n/a	1920	6
4788.2.ob	$\chi_{4788}(1021, \cdot)$	n/a	960	6

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4788))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4788)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(399))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(684))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(798))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1197))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1596))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2394))$$^{\oplus 2}$