Space of modular forms of level 672 and weight 4

• Label: 672.4
• Level: 672
• Weight: 4
• Dimension: 14804
• Nonzero newspaces: 24
• Sturm bound: 98304
• Trace bound: 14

Defining parameters

Level:	\( N \)	=	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(98304\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(672))\).

	Total	New	Old
Modular forms	37632	15004	22628
Cusp forms	36096	14804	21292
Eisenstein series	1536	200	1336

Trace form

14804 * q - 14 * q^3 - 32 * q^4 + 8 * q^5 - 16 * q^6 + 16 * q^9 + 448 * q^10 - 112 * q^12 - 504 * q^13 - 416 * q^14 - 140 * q^15 - 1232 * q^16 - 416 * q^17 - 160 * q^18 - 76 * q^19 + 320 * q^20 - 36 * q^21 + 704 * q^22 + 1968 * q^23 - 104 * q^24 + 628 * q^25 + 80 * q^26 - 800 * q^27 + 720 * q^28 - 568 * q^29 + 2240 * q^30 - 4284 * q^31 + 2480 * q^32 - 124 * q^33 + 2096 * q^34 - 912 * q^35 - 1200 * q^36 + 1288 * q^37 - 880 * q^38 + 1976 * q^39 - 3312 * q^40 + 2128 * q^41 - 920 * q^42 + 6456 * q^43 - 2000 * q^44 + 3784 * q^45 - 32 * q^46 + 408 * q^47 + 4872 * q^48 - 5404 * q^49 - 5712 * q^50 - 3366 * q^51 - 6656 * q^52 - 1272 * q^53 - 8 * q^54 - 4416 * q^55 + 392 * q^56 - 3608 * q^57 + 4720 * q^58 + 1376 * q^59 - 712 * q^60 - 7992 * q^61 + 5856 * q^62 + 798 * q^63 + 19744 * q^64 + 7408 * q^65 + 11984 * q^66 + 10412 * q^67 + 10064 * q^68 + 1344 * q^69 + 2768 * q^70 + 1928 * q^71 - 2776 * q^72 - 9664 * q^73 - 13888 * q^74 - 8592 * q^75 - 20512 * q^76 - 64 * q^77 - 13736 * q^78 - 11420 * q^79 - 22672 * q^80 - 8112 * q^81 - 11712 * q^82 - 2432 * q^84 + 3152 * q^85 - 4736 * q^86 + 4816 * q^87 - 1264 * q^88 - 5656 * q^90 - 976 * q^91 + 2480 * q^92 - 1080 * q^93 - 22928 * q^94 - 1384 * q^95 - 21224 * q^96 - 3680 * q^97 - 13568 * q^98 + 17740 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(672))\)

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
672.4.a	\(\chi_{672}(1, \cdot)\)	672.4.a.a	1	1
		672.4.a.b	1
		672.4.a.c	1
		672.4.a.d	1
		672.4.a.e	2
		672.4.a.f	2
		672.4.a.g	2
		672.4.a.h	2
		672.4.a.i	2
		672.4.a.j	2
		672.4.a.k	2
		672.4.a.l	2
		672.4.a.m	2
		672.4.a.n	2
		672.4.a.o	3
		672.4.a.p	3
		672.4.a.q	3
		672.4.a.r	3
672.4.b	\(\chi_{672}(223, \cdot)\)	672.4.b.a	24	1
		672.4.b.b	24
672.4.c	\(\chi_{672}(337, \cdot)\)	672.4.c.a	16	1
		672.4.c.b	20
672.4.h	\(\chi_{672}(575, \cdot)\)	672.4.h.a	36	1
		672.4.h.b	36
672.4.i	\(\chi_{672}(209, \cdot)\)	672.4.i.a	4	1
		672.4.i.b	8
		672.4.i.c	80
672.4.j	\(\chi_{672}(239, \cdot)\)	672.4.j.a	72	1
672.4.k	\(\chi_{672}(545, \cdot)\)	672.4.k.a	8	1
		672.4.k.b	8
		672.4.k.c	16
		672.4.k.d	16
		672.4.k.e	48
672.4.p	\(\chi_{672}(559, \cdot)\)	672.4.p.a	48	1
672.4.q	\(\chi_{672}(193, \cdot)\)	672.4.q.a	2	2
		672.4.q.b	2
		672.4.q.c	4
		672.4.q.d	4
		672.4.q.e	6
		672.4.q.f	6
		672.4.q.g	10
		672.4.q.h	10
		672.4.q.i	12
		672.4.q.j	12
		672.4.q.k	14
		672.4.q.l	14
672.4.s	\(\chi_{672}(71, \cdot)\)	None	0	2
672.4.u	\(\chi_{672}(55, \cdot)\)	None	0	2
672.4.w	\(\chi_{672}(169, \cdot)\)	None	0	2
672.4.y	\(\chi_{672}(41, \cdot)\)	None	0	2
672.4.bb	\(\chi_{672}(271, \cdot)\)	672.4.bb.a	96	2
672.4.bc	\(\chi_{672}(257, \cdot)\)	n/a	192	2
672.4.bd	\(\chi_{672}(431, \cdot)\)	n/a	184	2
672.4.bi	\(\chi_{672}(17, \cdot)\)	n/a	184	2
672.4.bj	\(\chi_{672}(95, \cdot)\)	n/a	192	2
672.4.bk	\(\chi_{672}(529, \cdot)\)	672.4.bk.a	96	2
672.4.bl	\(\chi_{672}(31, \cdot)\)	672.4.bl.a	48	2
		672.4.bl.b	48
672.4.bo	\(\chi_{672}(125, \cdot)\)	n/a	1520	4
672.4.bq	\(\chi_{672}(85, \cdot)\)	n/a	576	4
672.4.bs	\(\chi_{672}(155, \cdot)\)	n/a	1152	4
672.4.bu	\(\chi_{672}(139, \cdot)\)	n/a	768	4
672.4.bw	\(\chi_{672}(89, \cdot)\)	None	0	4
672.4.by	\(\chi_{672}(25, \cdot)\)	None	0	4
672.4.ca	\(\chi_{672}(103, \cdot)\)	None	0	4
672.4.cc	\(\chi_{672}(23, \cdot)\)	None	0	4
672.4.cf	\(\chi_{672}(19, \cdot)\)	n/a	1536	8
672.4.ch	\(\chi_{672}(11, \cdot)\)	n/a	3040	8
672.4.cj	\(\chi_{672}(37, \cdot)\)	n/a	1536	8
672.4.cl	\(\chi_{672}(5, \cdot)\)	n/a	3040	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(672))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(672)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 1}\)