Space of modular forms of level 630 and weight 4

• Label: 630.4
• Level: 630
• Weight: 4
• Dimension: 7210
• Nonzero newspaces: 30
• Sturm bound: 82944
• Trace bound: 15

Defining parameters

Level:	\( N \)	=	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(82944\)
Trace bound:			\(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(630))\).

	Total	New	Old
Modular forms	31872	7210	24662
Cusp forms	30336	7210	23126
Eisenstein series	1536	0	1536

Trace form

7210 * q + 12 * q^2 + 12 * q^3 - 24 * q^4 + 58 * q^5 - 72 * q^6 + 92 * q^7 - 48 * q^8 - 164 * q^9 + 32 * q^10 - 16 * q^11 - 32 * q^12 - 152 * q^13 + 592 * q^14 - 252 * q^15 - 224 * q^16 - 1560 * q^17 - 112 * q^18 - 632 * q^19 + 128 * q^20 - 720 * q^21 - 168 * q^22 - 732 * q^23 - 288 * q^24 + 692 * q^25 + 48 * q^26 + 480 * q^27 + 224 * q^28 - 108 * q^29 + 264 * q^30 + 1380 * q^31 + 192 * q^32 + 916 * q^33 + 832 * q^34 - 2084 * q^35 + 1168 * q^36 + 616 * q^37 + 672 * q^38 - 656 * q^39 - 384 * q^40 - 1648 * q^41 + 800 * q^42 - 3332 * q^43 - 272 * q^44 + 4244 * q^45 - 736 * q^46 + 5676 * q^47 + 448 * q^48 + 7146 * q^49 - 812 * q^50 - 6492 * q^51 + 2176 * q^52 + 864 * q^53 - 2040 * q^54 + 5644 * q^55 - 640 * q^56 - 2356 * q^57 - 696 * q^58 + 5900 * q^59 + 4336 * q^60 - 1372 * q^61 + 5616 * q^62 + 18436 * q^63 + 1152 * q^64 + 5328 * q^65 + 10560 * q^66 + 2800 * q^67 + 2544 * q^68 + 9392 * q^69 - 3132 * q^70 - 11520 * q^71 - 96 * q^72 - 2480 * q^73 - 12424 * q^74 - 21156 * q^75 - 6944 * q^76 - 28980 * q^77 - 21520 * q^78 - 14540 * q^79 - 800 * q^80 - 3532 * q^81 - 10584 * q^82 - 1932 * q^83 + 1872 * q^84 + 1564 * q^85 + 7576 * q^86 - 2936 * q^87 - 2208 * q^88 + 9424 * q^89 - 1376 * q^90 + 5500 * q^91 + 1152 * q^92 + 7304 * q^93 + 7664 * q^94 + 10026 * q^95 + 1792 * q^96 + 10552 * q^97 + 15828 * q^98 + 16720 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(630))\)

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
630.4.a	\(\chi_{630}(1, \cdot)\)	630.4.a.a	1	1
		630.4.a.b	1
		630.4.a.c	1
		630.4.a.d	1
		630.4.a.e	1
		630.4.a.f	1
		630.4.a.g	1
		630.4.a.h	1
		630.4.a.i	1
		630.4.a.j	1
		630.4.a.k	1
		630.4.a.l	1
		630.4.a.m	1
		630.4.a.n	1
		630.4.a.o	1
		630.4.a.p	1
		630.4.a.q	1
		630.4.a.r	1
		630.4.a.s	1
		630.4.a.t	1
		630.4.a.u	1
		630.4.a.v	1
		630.4.a.w	1
		630.4.a.x	1
		630.4.a.y	2
		630.4.a.z	2
		630.4.a.ba	2
630.4.b	\(\chi_{630}(251, \cdot)\)	630.4.b.a	16	1
		630.4.b.b	16
630.4.d	\(\chi_{630}(629, \cdot)\)	630.4.d.a	24	1
		630.4.d.b	24
630.4.g	\(\chi_{630}(379, \cdot)\)	630.4.g.a	2	1
		630.4.g.b	2
		630.4.g.c	2
		630.4.g.d	4
		630.4.g.e	4
		630.4.g.f	6
		630.4.g.g	6
		630.4.g.h	6
		630.4.g.i	6
		630.4.g.j	6
630.4.i	\(\chi_{630}(121, \cdot)\)	n/a	192	2
630.4.j	\(\chi_{630}(211, \cdot)\)	n/a	144	2
630.4.k	\(\chi_{630}(361, \cdot)\)	630.4.k.a	2	2
		630.4.k.b	2
		630.4.k.c	2
		630.4.k.d	2
		630.4.k.e	2
		630.4.k.f	2
		630.4.k.g	2
		630.4.k.h	2
		630.4.k.i	2
		630.4.k.j	2
		630.4.k.k	4
		630.4.k.l	4
		630.4.k.m	4
		630.4.k.n	4
		630.4.k.o	6
		630.4.k.p	6
		630.4.k.q	6
		630.4.k.r	6
		630.4.k.s	10
		630.4.k.t	10
630.4.l	\(\chi_{630}(331, \cdot)\)	n/a	192	2
630.4.m	\(\chi_{630}(197, \cdot)\)	630.4.m.a	16	2
		630.4.m.b	16
		630.4.m.c	20
		630.4.m.d	20
630.4.p	\(\chi_{630}(307, \cdot)\)	n/a	120	2
630.4.r	\(\chi_{630}(59, \cdot)\)	n/a	288	2
630.4.t	\(\chi_{630}(311, \cdot)\)	n/a	192	2
630.4.u	\(\chi_{630}(109, \cdot)\)	n/a	120	2
630.4.z	\(\chi_{630}(169, \cdot)\)	n/a	216	2
630.4.ba	\(\chi_{630}(499, \cdot)\)	n/a	288	2
630.4.be	\(\chi_{630}(341, \cdot)\)	630.4.be.a	32	2
		630.4.be.b	32
630.4.bf	\(\chi_{630}(209, \cdot)\)	n/a	288	2
630.4.bi	\(\chi_{630}(479, \cdot)\)	n/a	288	2
630.4.bk	\(\chi_{630}(101, \cdot)\)	n/a	192	2
630.4.bl	\(\chi_{630}(41, \cdot)\)	n/a	192	2
630.4.bo	\(\chi_{630}(89, \cdot)\)	630.4.bo.a	48	2
		630.4.bo.b	48
630.4.bq	\(\chi_{630}(79, \cdot)\)	n/a	288	2
630.4.bt	\(\chi_{630}(317, \cdot)\)	n/a	576	4
630.4.bv	\(\chi_{630}(73, \cdot)\)	n/a	240	4
630.4.bw	\(\chi_{630}(103, \cdot)\)	n/a	576	4
630.4.bz	\(\chi_{630}(13, \cdot)\)	n/a	576	4
630.4.ca	\(\chi_{630}(113, \cdot)\)	n/a	432	4
630.4.cd	\(\chi_{630}(23, \cdot)\)	n/a	576	4
630.4.ce	\(\chi_{630}(53, \cdot)\)	n/a	192	4
630.4.cg	\(\chi_{630}(157, \cdot)\)	n/a	576	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(630))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(630)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)