Space of modular forms of level 4650 and weight 2

• Label: 4650.2
• Level: 4650
• Weight: 2
• Dimension: 132446
• Nonzero newspaces: 84
• Sturm bound: 2304000

Defining parameters

Level:	$N$	=	$4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31$
Weight:	$k$	=	$2$
Nonzero newspaces:			$84$
Sturm bound:			$2304000$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4650))$.

	Total	New	Old
Modular forms	582720	132446	450274
Cusp forms	569281	132446	436835
Eisenstein series	13439	0	13439

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4650))$

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
4650.2.a	$\chi_{4650}(1, \cdot)$	4650.2.a.a	1	1
		4650.2.a.b	1
		4650.2.a.c	1
		4650.2.a.d	1
		4650.2.a.e	1
		4650.2.a.f	1
		4650.2.a.g	1
		4650.2.a.h	1
		4650.2.a.i	1
		4650.2.a.j	1
		4650.2.a.k	1
		4650.2.a.l	1
		4650.2.a.m	1
		4650.2.a.n	1
		4650.2.a.o	1
		4650.2.a.p	1
		4650.2.a.q	1
		4650.2.a.r	1
		4650.2.a.s	1
		4650.2.a.t	1
		4650.2.a.u	1
		4650.2.a.v	1
		4650.2.a.w	1
		4650.2.a.x	1
		4650.2.a.y	1
		4650.2.a.z	1
		4650.2.a.ba	1
		4650.2.a.bb	1
		4650.2.a.bc	1
		4650.2.a.bd	1
		4650.2.a.be	1
		4650.2.a.bf	1
		4650.2.a.bg	1
		4650.2.a.bh	1
		4650.2.a.bi	1
		4650.2.a.bj	1
		4650.2.a.bk	1
		4650.2.a.bl	1
		4650.2.a.bm	1
		4650.2.a.bn	1
		4650.2.a.bo	1
		4650.2.a.bp	1
		4650.2.a.bq	1
		4650.2.a.br	1
		4650.2.a.bs	1
		4650.2.a.bt	1
		4650.2.a.bu	1
		4650.2.a.bv	1
		4650.2.a.bw	1
		4650.2.a.bx	1
		4650.2.a.by	2
		4650.2.a.bz	2
		4650.2.a.ca	2
		4650.2.a.cb	2
		4650.2.a.cc	2
		4650.2.a.cd	2
		4650.2.a.ce	2
		4650.2.a.cf	2
		4650.2.a.cg	2
		4650.2.a.ch	2
		4650.2.a.ci	3
		4650.2.a.cj	3
		4650.2.a.ck	3
		4650.2.a.cl	3
4650.2.a.cm	3
4650.2.a.cn	3
4650.2.a.co	3
4650.2.a.cp	3
4650.2.d	$\chi_{4650}(3349, \cdot)$	4650.2.d.a	2	1
		4650.2.d.b	2
		4650.2.d.c	2
		4650.2.d.d	2
		4650.2.d.e	2
		4650.2.d.f	2
		4650.2.d.g	2
		4650.2.d.h	2
		4650.2.d.i	2
		4650.2.d.j	2
		4650.2.d.k	2
		4650.2.d.l	2
		4650.2.d.m	2
		4650.2.d.n	2
		4650.2.d.o	2
		4650.2.d.p	2
		4650.2.d.q	2
		4650.2.d.r	2
		4650.2.d.s	2
		4650.2.d.t	2
		4650.2.d.u	2
		4650.2.d.v	2
		4650.2.d.w	2
		4650.2.d.x	2
		4650.2.d.y	2
		4650.2.d.z	2
		4650.2.d.ba	2
		4650.2.d.bb	2
		4650.2.d.bc	4
		4650.2.d.bd	4
		4650.2.d.be	4
		4650.2.d.bf	4
		4650.2.d.bg	4
		4650.2.d.bh	4
		4650.2.d.bi	6
		4650.2.d.bj	6
4650.2.e	$\chi_{4650}(4649, \cdot)$	n/a	192	1
4650.2.h	$\chi_{4650}(1301, \cdot)$	n/a	204	1
4650.2.i	$\chi_{4650}(3001, \cdot)$	n/a	204	2
4650.2.j	$\chi_{4650}(2357, \cdot)$	n/a	360	2
4650.2.k	$\chi_{4650}(2107, \cdot)$	n/a	192	2
4650.2.n	$\chi_{4650}(721, \cdot)$	n/a	640	4
4650.2.o	$\chi_{4650}(901, \cdot)$	n/a	400	4
4650.2.p	$\chi_{4650}(1831, \cdot)$	n/a	640	4
4650.2.q	$\chi_{4650}(1771, \cdot)$	n/a	640	4
4650.2.r	$\chi_{4650}(481, \cdot)$	n/a	640	4
4650.2.s	$\chi_{4650}(931, \cdot)$	n/a	608	4
4650.2.t	$\chi_{4650}(2351, \cdot)$	n/a	404	2
4650.2.w	$\chi_{4650}(1049, \cdot)$	n/a	384	2
4650.2.x	$\chi_{4650}(1699, \cdot)$	n/a	192	2
4650.2.ba	$\chi_{4650}(929, \cdot)$	n/a	1280	4
4650.2.bb	$\chi_{4650}(559, \cdot)$	n/a	592	4
4650.2.bg	$\chi_{4650}(581, \cdot)$	n/a	1280	4
4650.2.bh	$\chi_{4650}(401, \cdot)$	n/a	816	4
4650.2.bi	$\chi_{4650}(3191, \cdot)$	n/a	1280	4
4650.2.bj	$\chi_{4650}(461, \cdot)$	n/a	1280	4
4650.2.bs	$\chi_{4650}(1391, \cdot)$	n/a	1280	4
4650.2.bv	$\chi_{4650}(109, \cdot)$	n/a	640	4
4650.2.bw	$\chi_{4650}(89, \cdot)$	n/a	1280	4
4650.2.bx	$\chi_{4650}(959, \cdot)$	n/a	1280	4
4650.2.by	$\chi_{4650}(449, \cdot)$	n/a	768	4
4650.2.bz	$\chi_{4650}(2209, \cdot)$	n/a	640	4
4650.2.ca	$\chi_{4650}(349, \cdot)$	n/a	384	4
4650.2.cb	$\chi_{4650}(469, \cdot)$	n/a	640	4
4650.2.cc	$\chi_{4650}(1889, \cdot)$	n/a	1280	4
4650.2.cl	$\chi_{4650}(29, \cdot)$	n/a	1280	4
4650.2.cm	$\chi_{4650}(529, \cdot)$	n/a	640	4
4650.2.cn	$\chi_{4650}(371, \cdot)$	n/a	1280	4
4650.2.cs	$\chi_{4650}(3157, \cdot)$	n/a	384	4
4650.2.ct	$\chi_{4650}(707, \cdot)$	n/a	768	4
4650.2.cu	$\chi_{4650}(211, \cdot)$	n/a	1280	8
4650.2.cv	$\chi_{4650}(1291, \cdot)$	n/a	1280	8
4650.2.cw	$\chi_{4650}(661, \cdot)$	n/a	1280	8
4650.2.cx	$\chi_{4650}(751, \cdot)$	n/a	816	8
4650.2.cy	$\chi_{4650}(391, \cdot)$	n/a	1280	8
4650.2.cz	$\chi_{4650}(121, \cdot)$	n/a	1280	8
4650.2.da	$\chi_{4650}(337, \cdot)$	n/a	1280	8
4650.2.db	$\chi_{4650}(233, \cdot)$	n/a	2560	8
4650.2.dm	$\chi_{4650}(977, \cdot)$	n/a	2560	8
4650.2.dn	$\chi_{4650}(247, \cdot)$	n/a	1280	8
4650.2.do	$\chi_{4650}(277, \cdot)$	n/a	1280	8
4650.2.dp	$\chi_{4650}(457, \cdot)$	n/a	768	8
4650.2.dq	$\chi_{4650}(497, \cdot)$	n/a	2400	8
4650.2.dr	$\chi_{4650}(407, \cdot)$	n/a	1536	8
4650.2.ds	$\chi_{4650}(1163, \cdot)$	n/a	2560	8
4650.2.dt	$\chi_{4650}(463, \cdot)$	n/a	1280	8
4650.2.du	$\chi_{4650}(523, \cdot)$	n/a	1280	8
4650.2.dv	$\chi_{4650}(47, \cdot)$	n/a	2560	8
4650.2.ea	$\chi_{4650}(161, \cdot)$	n/a	2560	8
4650.2.eb	$\chi_{4650}(1309, \cdot)$	n/a	1280	8
4650.2.ec	$\chi_{4650}(239, \cdot)$	n/a	2560	8
4650.2.el	$\chi_{4650}(179, \cdot)$	n/a	2560	8
4650.2.em	$\chi_{4650}(19, \cdot)$	n/a	1280	8
4650.2.en	$\chi_{4650}(919, \cdot)$	n/a	1280	8
4650.2.eo	$\chi_{4650}(49, \cdot)$	n/a	768	8
4650.2.ep	$\chi_{4650}(269, \cdot)$	n/a	2560	8
4650.2.eq	$\chi_{4650}(1199, \cdot)$	n/a	1536	8
4650.2.er	$\chi_{4650}(569, \cdot)$	n/a	2560	8
4650.2.es	$\chi_{4650}(169, \cdot)$	n/a	1280	8
4650.2.ev	$\chi_{4650}(611, \cdot)$	n/a	2560	8
4650.2.fe	$\chi_{4650}(641, \cdot)$	n/a	2560	8
4650.2.ff	$\chi_{4650}(251, \cdot)$	n/a	1616	8
4650.2.fg	$\chi_{4650}(11, \cdot)$	n/a	2560	8
4650.2.fh	$\chi_{4650}(911, \cdot)$	n/a	2560	8
4650.2.fm	$\chi_{4650}(439, \cdot)$	n/a	1280	8
4650.2.fn	$\chi_{4650}(119, \cdot)$	n/a	2560	8
4650.2.fq	$\chi_{4650}(127, \cdot)$	n/a	2560	16
4650.2.fr	$\chi_{4650}(227, \cdot)$	n/a	5120	16
4650.2.fs	$\chi_{4650}(107, \cdot)$	n/a	3072	16
4650.2.ft	$\chi_{4650}(377, \cdot)$	n/a	5120	16
4650.2.fu	$\chi_{4650}(43, \cdot)$	n/a	1536	16
4650.2.fv	$\chi_{4650}(13, \cdot)$	n/a	2560	16
4650.2.fw	$\chi_{4650}(37, \cdot)$	n/a	2560	16
4650.2.fx	$\chi_{4650}(173, \cdot)$	n/a	5120	16
4650.2.fy	$\chi_{4650}(803, \cdot)$	n/a	5120	16
4650.2.fz	$\chi_{4650}(73, \cdot)$	n/a	2560	16
4650.2.gk	$\chi_{4650}(113, \cdot)$	n/a	5120	16
4650.2.gl	$\chi_{4650}(613, \cdot)$	n/a	2560	16

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4650))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4650)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(93))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(186))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(310))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(465))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(775))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(930))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1550))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2325))$$^{\oplus 2}$