Space of modular forms of level 3528 and weight 1

• Label: 3528.1
• Level: 3528
• Weight: 1
• Dimension: 243
• Nonzero newspaces: 22
• Newform subspaces: 45
• Sturm bound: 677376
• Trace bound: 25

Defining parameters

Level:	$N$	=	$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	=	$1$
Nonzero newspaces:			$22$
Newform subspaces:			$45$
Sturm bound:			$677376$
Trace bound:			$25$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(\Gamma_1(3528))$.

	Total	New	Old
Modular forms	6658	1116	5542
Cusp forms	898	243	655
Eisenstein series	5760	873	4887

The following table gives the dimensions of subspaces with specified projective image type.

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	219	16	8	0

Trace form

243 * q + 3 * q^3 + 6 * q^4 + q^6 + 3 * q^8 - q^9 + 8 * q^10 + q^11 - 4 * q^12 + 4 * q^13 - 8 * q^15 + 6 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 13 * q^22 - 2 * q^23 + q^24 + 12 * q^25 - 4 * q^26 + 6 * q^27 + 2 * q^30 - 14 * q^31 + 3 * q^33 - q^34 - 15 * q^36 + 2 * q^37 - q^38 + 4 * q^39 - 32 * q^40 - 5 * q^41 + 5 * q^43 + 6 * q^44 + 2 * q^46 + 9 * q^48 + 46 * q^50 - 3 * q^51 + q^54 + 8 * q^55 + 11 * q^57 - 14 * q^58 - q^59 + 4 * q^60 - 27 * q^64 - 2 * q^65 + 2 * q^66 + 5 * q^67 - 3 * q^68 - 6 * q^70 + 4 * q^71 - 7 * q^72 + 8 * q^73 + 2 * q^74 + q^75 - 5 * q^76 + 32 * q^78 + 16 * q^79 - 9 * q^81 + 2 * q^82 - 2 * q^83 - q^86 - 17 * q^88 - 4 * q^90 - 32 * q^92 + 8 * q^95 - 2 * q^96 + 3 * q^97 + 10 * q^99

Decomposition of $S_{1}^{\mathrm{new}}(\Gamma_1(3528))$

We only show spaces with odd 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
3528.1.d	$\chi_{3528}(1961, \cdot)$	3528.1.d.a	2	1
		3528.1.d.b	2
3528.1.e	$\chi_{3528}(1763, \cdot)$	None	0	1
3528.1.f	$\chi_{3528}(2449, \cdot)$	None	0	1
3528.1.g	$\chi_{3528}(883, \cdot)$	3528.1.g.a	1	1
		3528.1.g.b	2
		3528.1.g.c	2
3528.1.l	$\chi_{3528}(685, \cdot)$	3528.1.l.a	4	1
3528.1.m	$\chi_{3528}(2647, \cdot)$	None	0	1
3528.1.n	$\chi_{3528}(197, \cdot)$	3528.1.n.a	4	1
3528.1.o	$\chi_{3528}(3527, \cdot)$	None	0	1
3528.1.u	$\chi_{3528}(803, \cdot)$	3528.1.u.a	16	2
3528.1.v	$\chi_{3528}(569, \cdot)$	None	0	2
3528.1.ba	$\chi_{3528}(67, \cdot)$	3528.1.ba.a	2	2
		3528.1.ba.b	2
		3528.1.ba.c	4
		3528.1.ba.d	4
		3528.1.ba.e	8
3528.1.bb	$\chi_{3528}(313, \cdot)$	None	0	2
3528.1.bc	$\chi_{3528}(215, \cdot)$	None	0	2
3528.1.bd	$\chi_{3528}(557, \cdot)$	3528.1.bd.a	8	2
3528.1.bg	$\chi_{3528}(1373, \cdot)$	3528.1.bg.a	8	2
3528.1.bh	$\chi_{3528}(1391, \cdot)$	None	0	2
3528.1.bi	$\chi_{3528}(1157, \cdot)$	3528.1.bi.a	8	2
3528.1.bj	$\chi_{3528}(1175, \cdot)$	None	0	2
3528.1.bn	$\chi_{3528}(1861, \cdot)$	None	0	2
3528.1.bo	$\chi_{3528}(655, \cdot)$	None	0	2
3528.1.bp	$\chi_{3528}(1501, \cdot)$	3528.1.bp.a	2	2
		3528.1.bp.b	2
		3528.1.bp.c	4
3528.1.bq	$\chi_{3528}(295, \cdot)$	None	0	2
3528.1.bv	$\chi_{3528}(2431, \cdot)$	None	0	2
3528.1.bw	$\chi_{3528}(325, \cdot)$	3528.1.bw.a	2	2
		3528.1.bw.b	4
		3528.1.bw.c	4
3528.1.bx	$\chi_{3528}(667, \cdot)$	3528.1.bx.a	2	2
		3528.1.bx.b	4
		3528.1.bx.c	4
3528.1.by	$\chi_{3528}(2089, \cdot)$	None	0	2
3528.1.cd	$\chi_{3528}(97, \cdot)$	None	0	2
3528.1.ce	$\chi_{3528}(2419, \cdot)$	3528.1.ce.a	2	2
		3528.1.ce.b	2
		3528.1.ce.c	4
		3528.1.ce.d	4
		3528.1.ce.e	8
3528.1.cf	$\chi_{3528}(1489, \cdot)$	None	0	2
3528.1.cg	$\chi_{3528}(2059, \cdot)$	3528.1.cg.a	2	2
		3528.1.cg.b	4
		3528.1.cg.c	4
		3528.1.cg.d	4
		3528.1.cg.e	8
3528.1.cl	$\chi_{3528}(785, \cdot)$	None	0	2
3528.1.cm	$\chi_{3528}(227, \cdot)$	3528.1.cm.a	16	2
3528.1.cn	$\chi_{3528}(1145, \cdot)$	None	0	2
3528.1.co	$\chi_{3528}(587, \cdot)$	3528.1.co.a	16	2
3528.1.ct	$\chi_{3528}(1403, \cdot)$	3528.1.ct.a	8	2
3528.1.cu	$\chi_{3528}(1745, \cdot)$	3528.1.cu.a	4	2
3528.1.cv	$\chi_{3528}(79, \cdot)$	None	0	2
3528.1.cw	$\chi_{3528}(2077, \cdot)$	3528.1.cw.a	2	2
		3528.1.cw.b	2
		3528.1.cw.c	4
3528.1.da	$\chi_{3528}(815, \cdot)$	None	0	2
3528.1.db	$\chi_{3528}(1733, \cdot)$	3528.1.db.a	8	2
3528.1.de	$\chi_{3528}(503, \cdot)$	None	0	6
3528.1.df	$\chi_{3528}(701, \cdot)$	None	0	6
3528.1.dg	$\chi_{3528}(127, \cdot)$	None	0	6
3528.1.dh	$\chi_{3528}(181, \cdot)$	3528.1.dh.a	12	6
3528.1.dm	$\chi_{3528}(379, \cdot)$	None	0	6
3528.1.dn	$\chi_{3528}(433, \cdot)$	None	0	6
3528.1.do	$\chi_{3528}(251, \cdot)$	None	0	6
3528.1.dp	$\chi_{3528}(449, \cdot)$	None	0	6
3528.1.dw	$\chi_{3528}(221, \cdot)$	None	0	12
3528.1.dx	$\chi_{3528}(47, \cdot)$	None	0	12
3528.1.eb	$\chi_{3528}(61, \cdot)$	None	0	12
3528.1.ec	$\chi_{3528}(319, \cdot)$	None	0	12
3528.1.ed	$\chi_{3528}(233, \cdot)$	None	0	12
3528.1.ee	$\chi_{3528}(395, \cdot)$	None	0	12
3528.1.ej	$\chi_{3528}(83, \cdot)$	None	0	12
3528.1.ek	$\chi_{3528}(137, \cdot)$	None	0	12
3528.1.el	$\chi_{3528}(131, \cdot)$	None	0	12
3528.1.em	$\chi_{3528}(113, \cdot)$	None	0	12
3528.1.er	$\chi_{3528}(43, \cdot)$	None	0	12
3528.1.es	$\chi_{3528}(241, \cdot)$	None	0	12
3528.1.et	$\chi_{3528}(403, \cdot)$	None	0	12
3528.1.eu	$\chi_{3528}(265, \cdot)$	None	0	12
3528.1.ez	$\chi_{3528}(73, \cdot)$	None	0	12
3528.1.fa	$\chi_{3528}(163, \cdot)$	None	0	12
3528.1.fb	$\chi_{3528}(397, \cdot)$	3528.1.fb.a	24	12
3528.1.fc	$\chi_{3528}(415, \cdot)$	None	0	12
3528.1.fh	$\chi_{3528}(463, \cdot)$	None	0	12
3528.1.fi	$\chi_{3528}(229, \cdot)$	None	0	12
3528.1.fj	$\chi_{3528}(151, \cdot)$	None	0	12
3528.1.fk	$\chi_{3528}(13, \cdot)$	None	0	12
3528.1.fo	$\chi_{3528}(167, \cdot)$	None	0	12
3528.1.fp	$\chi_{3528}(149, \cdot)$	None	0	12
3528.1.fq	$\chi_{3528}(383, \cdot)$	None	0	12
3528.1.fr	$\chi_{3528}(29, \cdot)$	None	0	12
3528.1.fu	$\chi_{3528}(53, \cdot)$	None	0	12
3528.1.fv	$\chi_{3528}(143, \cdot)$	None	0	12
3528.1.fw	$\chi_{3528}(409, \cdot)$	None	0	12
3528.1.fx	$\chi_{3528}(331, \cdot)$	None	0	12
3528.1.gc	$\chi_{3528}(65, \cdot)$	None	0	12
3528.1.gd	$\chi_{3528}(59, \cdot)$	None	0	12

Decomposition of $S_{1}^{\mathrm{old}}(\Gamma_1(3528))$ into lower level spaces

$S_{1}^{\mathrm{old}}(\Gamma_1(3528)) \cong$ $S_{1}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 36}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 27}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 18}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 18}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 24}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 9}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 18}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 9}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 16}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(42))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(49))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(84))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(98))$$^{\oplus 9}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(126))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(147))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(168))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(196))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(252))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(294))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(392))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(441))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(504))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(588))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(882))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(1176))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(1764))$$^{\oplus 2}$