Space of modular forms of level 4655 and weight 2

• Label: 4655.2
• Level: 4655
• Weight: 2
• Dimension: 735722
• Nonzero newspaces: 96
• Sturm bound: 3386880

Defining parameters

Level:	$N$	=	$4655 = 5 \cdot 7^{2} \cdot 19$
Weight:	$k$	=	$2$
Nonzero newspaces:			$96$
Sturm bound:			$3386880$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4655))$.

	Total	New	Old
Modular forms	855360	745618	109742
Cusp forms	838081	735722	102359
Eisenstein series	17279	9896	7383

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4655))$

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
4655.2.a	$\chi_{4655}(1, \cdot)$	4655.2.a.a	1	1
		4655.2.a.b	1
		4655.2.a.c	1
		4655.2.a.d	1
		4655.2.a.e	1
		4655.2.a.f	1
		4655.2.a.g	1
		4655.2.a.h	1
		4655.2.a.i	1
		4655.2.a.j	1
		4655.2.a.k	1
		4655.2.a.l	1
		4655.2.a.m	1
		4655.2.a.n	1
		4655.2.a.o	1
		4655.2.a.p	1
		4655.2.a.q	1
		4655.2.a.r	1
		4655.2.a.s	1
		4655.2.a.t	2
		4655.2.a.u	3
		4655.2.a.v	3
		4655.2.a.w	3
		4655.2.a.x	3
		4655.2.a.y	4
		4655.2.a.z	4
		4655.2.a.ba	4
		4655.2.a.bb	4
		4655.2.a.bc	6
		4655.2.a.bd	7
		4655.2.a.be	8
		4655.2.a.bf	8
		4655.2.a.bg	8
		4655.2.a.bh	8
		4655.2.a.bi	8
		4655.2.a.bj	10
		4655.2.a.bk	10
		4655.2.a.bl	11
		4655.2.a.bm	11
		4655.2.a.bn	12
		4655.2.a.bo	12
		4655.2.a.bp	13
		4655.2.a.bq	13
		4655.2.a.br	26
		4655.2.a.bs	26
4655.2.b	$\chi_{4655}(2794, \cdot)$	n/a	368	1
4655.2.d	$\chi_{4655}(1861, \cdot)$	n/a	264	1
4655.2.g	$\chi_{4655}(4654, \cdot)$	n/a	392	1
4655.2.i	$\chi_{4655}(3431, \cdot)$	n/a	544	2
4655.2.j	$\chi_{4655}(2186, \cdot)$	n/a	480	2
4655.2.k	$\chi_{4655}(961, \cdot)$	n/a	536	2
4655.2.l	$\chi_{4655}(1341, \cdot)$	n/a	536	2
4655.2.m	$\chi_{4655}(2547, \cdot)$	n/a	720	2
4655.2.p	$\chi_{4655}(1177, \cdot)$	n/a	800	2
4655.2.r	$\chi_{4655}(411, \cdot)$	n/a	536	2
4655.2.t	$\chi_{4655}(4134, \cdot)$	n/a	784	2
4655.2.v	$\chi_{4655}(2824, \cdot)$	n/a	784	2
4655.2.y	$\chi_{4655}(2089, \cdot)$	n/a	784	2
4655.2.ba	$\chi_{4655}(734, \cdot)$	n/a	784	2
4655.2.bd	$\chi_{4655}(3754, \cdot)$	n/a	784	2
4655.2.bg	$\chi_{4655}(3951, \cdot)$	n/a	536	2
4655.2.bi	$\chi_{4655}(2596, \cdot)$	n/a	528	2
4655.2.bk	$\chi_{4655}(1569, \cdot)$	n/a	800	2
4655.2.bm	$\chi_{4655}(324, \cdot)$	n/a	720	2
4655.2.bn	$\chi_{4655}(31, \cdot)$	n/a	536	2
4655.2.bq	$\chi_{4655}(3204, \cdot)$	n/a	784	2
4655.2.bs	$\chi_{4655}(666, \cdot)$	n/a	2016	6
4655.2.bt	$\chi_{4655}(606, \cdot)$	n/a	1596	6
4655.2.bu	$\chi_{4655}(491, \cdot)$	n/a	1644	6
4655.2.bv	$\chi_{4655}(226, \cdot)$	n/a	1596	6
4655.2.bw	$\chi_{4655}(312, \cdot)$	n/a	1568	4
4655.2.bz	$\chi_{4655}(558, \cdot)$	n/a	1568	4
4655.2.ca	$\chi_{4655}(362, \cdot)$	n/a	1440	4
4655.2.cc	$\chi_{4655}(753, \cdot)$	n/a	1568	4
4655.2.ce	$\chi_{4655}(1912, \cdot)$	n/a	1600	4
4655.2.ch	$\chi_{4655}(68, \cdot)$	n/a	1568	4
4655.2.cj	$\chi_{4655}(1322, \cdot)$	n/a	1568	4
4655.2.cl	$\chi_{4655}(18, \cdot)$	n/a	1568	4
4655.2.cn	$\chi_{4655}(664, \cdot)$	n/a	3336	6
4655.2.cq	$\chi_{4655}(531, \cdot)$	n/a	2256	6
4655.2.cs	$\chi_{4655}(134, \cdot)$	n/a	3024	6
4655.2.cw	$\chi_{4655}(509, \cdot)$	n/a	2352	6
4655.2.cx	$\chi_{4655}(489, \cdot)$	n/a	2352	6
4655.2.cz	$\chi_{4655}(129, \cdot)$	n/a	2352	6
4655.2.dc	$\chi_{4655}(146, \cdot)$	n/a	1608	6
4655.2.df	$\chi_{4655}(656, \cdot)$	n/a	1596	6
4655.2.dg	$\chi_{4655}(99, \cdot)$	n/a	2400	6
4655.2.dj	$\chi_{4655}(214, \cdot)$	n/a	2352	6
4655.2.dk	$\chi_{4655}(814, \cdot)$	n/a	2352	6
4655.2.dm	$\chi_{4655}(166, \cdot)$	n/a	1596	6
4655.2.do	$\chi_{4655}(11, \cdot)$	n/a	4464	12
4655.2.dp	$\chi_{4655}(296, \cdot)$	n/a	4464	12
4655.2.dq	$\chi_{4655}(191, \cdot)$	n/a	4032	12
4655.2.dr	$\chi_{4655}(106, \cdot)$	n/a	4512	12
4655.2.ds	$\chi_{4655}(113, \cdot)$	n/a	6672	12
4655.2.dv	$\chi_{4655}(153, \cdot)$	n/a	6048	12
4655.2.dw	$\chi_{4655}(508, \cdot)$	n/a	4704	12
4655.2.dy	$\chi_{4655}(148, \cdot)$	n/a	4800	12
4655.2.ea	$\chi_{4655}(313, \cdot)$	n/a	4704	12
4655.2.ec	$\chi_{4655}(538, \cdot)$	n/a	4704	12
4655.2.ef	$\chi_{4655}(803, \cdot)$	n/a	4704	12
4655.2.eh	$\chi_{4655}(67, \cdot)$	n/a	4704	12
4655.2.ej	$\chi_{4655}(544, \cdot)$	n/a	6672	12
4655.2.em	$\chi_{4655}(236, \cdot)$	n/a	4464	12
4655.2.en	$\chi_{4655}(39, \cdot)$	n/a	6048	12
4655.2.ep	$\chi_{4655}(64, \cdot)$	n/a	6672	12
4655.2.er	$\chi_{4655}(426, \cdot)$	n/a	4512	12
4655.2.et	$\chi_{4655}(341, \cdot)$	n/a	4464	12
4655.2.ew	$\chi_{4655}(429, \cdot)$	n/a	6672	12
4655.2.ez	$\chi_{4655}(69, \cdot)$	n/a	6672	12
4655.2.fb	$\chi_{4655}(94, \cdot)$	n/a	6672	12
4655.2.fe	$\chi_{4655}(164, \cdot)$	n/a	6672	12
4655.2.fg	$\chi_{4655}(144, \cdot)$	n/a	6672	12
4655.2.fi	$\chi_{4655}(1076, \cdot)$	n/a	4464	12
4655.2.fk	$\chi_{4655}(16, \cdot)$	n/a	13464	36
4655.2.fl	$\chi_{4655}(81, \cdot)$	n/a	13464	36
4655.2.fm	$\chi_{4655}(36, \cdot)$	n/a	13392	36
4655.2.fn	$\chi_{4655}(37, \cdot)$	n/a	13344	24
4655.2.fp	$\chi_{4655}(83, \cdot)$	n/a	13344	24
4655.2.fr	$\chi_{4655}(467, \cdot)$	n/a	13344	24
4655.2.fu	$\chi_{4655}(8, \cdot)$	n/a	13344	24
4655.2.fw	$\chi_{4655}(88, \cdot)$	n/a	13344	24
4655.2.fy	$\chi_{4655}(248, \cdot)$	n/a	12096	24
4655.2.fz	$\chi_{4655}(87, \cdot)$	n/a	13344	24
4655.2.gc	$\chi_{4655}(107, \cdot)$	n/a	13344	24
4655.2.gd	$\chi_{4655}(241, \cdot)$	n/a	13464	36
4655.2.gf	$\chi_{4655}(4, \cdot)$	n/a	20016	36
4655.2.gh	$\chi_{4655}(169, \cdot)$	n/a	20016	36
4655.2.gk	$\chi_{4655}(9, \cdot)$	n/a	20016	36
4655.2.gl	$\chi_{4655}(41, \cdot)$	n/a	13392	36
4655.2.go	$\chi_{4655}(136, \cdot)$	n/a	13464	36
4655.2.gq	$\chi_{4655}(299, \cdot)$	n/a	20016	36
4655.2.gt	$\chi_{4655}(59, \cdot)$	n/a	20016	36
4655.2.gu	$\chi_{4655}(34, \cdot)$	n/a	20016	36
4655.2.gz	$\chi_{4655}(2, \cdot)$	n/a	40032	72
4655.2.hb	$\chi_{4655}(138, \cdot)$	n/a	40032	72
4655.2.hc	$\chi_{4655}(17, \cdot)$	n/a	40032	72
4655.2.he	$\chi_{4655}(62, \cdot)$	n/a	40032	72
4655.2.hg	$\chi_{4655}(72, \cdot)$	n/a	40032	72
4655.2.hi	$\chi_{4655}(22, \cdot)$	n/a	40032	72

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4655))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4655)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(665))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(931))$$^{\oplus 2}$