Space of modular forms of level 672 and weight 3

• Label: 672.3
• Level: 672
• Weight: 3
• Dimension: 9836
• Nonzero newspaces: 24
• Sturm bound: 73728
• Trace bound: 14

Defining parameters

Level:	\( N \)	=	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(73728\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(672))\).

	Total	New	Old
Modular forms	25344	10036	15308
Cusp forms	23808	9836	13972
Eisenstein series	1536	200	1336

Trace form

9836 * q - 10 * q^3 - 32 * q^4 + 16 * q^5 - 16 * q^6 - 32 * q^7 - 40 * q^9 - 192 * q^10 - 64 * q^11 - 112 * q^12 - 144 * q^13 - 32 * q^14 - 76 * q^15 + 48 * q^16 + 64 * q^17 + 32 * q^18 + 44 * q^19 + 320 * q^20 + 12 * q^21 + 512 * q^22 - 256 * q^23 + 408 * q^24 - 44 * q^25 + 400 * q^26 - 208 * q^27 + 80 * q^28 + 80 * q^29 + 96 * q^30 + 116 * q^31 - 80 * q^32 + 204 * q^33 - 208 * q^34 + 288 * q^35 - 176 * q^36 + 48 * q^37 - 560 * q^38 + 544 * q^39 - 752 * q^40 + 96 * q^41 - 40 * q^42 + 104 * q^43 - 208 * q^44 - 288 * q^45 - 32 * q^46 - 576 * q^47 - 120 * q^48 - 324 * q^49 + 624 * q^50 + 14 * q^51 + 1024 * q^52 - 880 * q^53 - 488 * q^54 + 552 * q^55 + 392 * q^56 - 400 * q^57 + 688 * q^58 + 640 * q^59 - 584 * q^60 - 144 * q^61 + 96 * q^62 + 210 * q^63 - 992 * q^64 + 160 * q^65 - 1168 * q^66 - 308 * q^67 - 1712 * q^68 + 272 * q^69 - 1360 * q^70 - 640 * q^71 - 856 * q^72 + 112 * q^73 - 2112 * q^74 - 44 * q^75 - 2080 * q^76 + 512 * q^77 - 1320 * q^78 - 300 * q^79 - 656 * q^80 + 520 * q^81 + 448 * q^82 + 320 * q^83 - 256 * q^84 + 1504 * q^85 + 896 * q^86 + 1732 * q^87 + 1552 * q^88 + 1024 * q^89 + 584 * q^90 + 848 * q^91 + 2480 * q^92 + 1432 * q^93 + 4976 * q^94 + 1152 * q^95 + 3608 * q^96 + 2000 * q^97 + 4096 * q^98 - 444 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(672))\)

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
672.3.d	\(\chi_{672}(449, \cdot)\)	672.3.d.a	4	1
		672.3.d.b	8
		672.3.d.c	12
		672.3.d.d	24
672.3.e	\(\chi_{672}(335, \cdot)\)	672.3.e.a	1	1
		672.3.e.b	1
		672.3.e.c	1
		672.3.e.d	1
		672.3.e.e	8
		672.3.e.f	48
672.3.f	\(\chi_{672}(97, \cdot)\)	672.3.f.a	16	1
		672.3.f.b	16
672.3.g	\(\chi_{672}(463, \cdot)\)	672.3.g.a	24	1
672.3.l	\(\chi_{672}(433, \cdot)\)	672.3.l.a	32	1
672.3.m	\(\chi_{672}(127, \cdot)\)	672.3.m.a	8	1
		672.3.m.b	16
672.3.n	\(\chi_{672}(113, \cdot)\)	672.3.n.a	48	1
672.3.o	\(\chi_{672}(671, \cdot)\)	672.3.o.a	32	1
		672.3.o.b	32
672.3.r	\(\chi_{672}(265, \cdot)\)	None	0	2
672.3.t	\(\chi_{672}(281, \cdot)\)	None	0	2
672.3.v	\(\chi_{672}(167, \cdot)\)	None	0	2
672.3.x	\(\chi_{672}(295, \cdot)\)	None	0	2
672.3.z	\(\chi_{672}(383, \cdot)\)	n/a	128	2
672.3.ba	\(\chi_{672}(305, \cdot)\)	n/a	120	2
672.3.be	\(\chi_{672}(319, \cdot)\)	672.3.be.a	16	2
		672.3.be.b	16
		672.3.be.c	16
		672.3.be.d	16
672.3.bf	\(\chi_{672}(145, \cdot)\)	672.3.bf.a	4	2
		672.3.bf.b	60
672.3.bg	\(\chi_{672}(79, \cdot)\)	672.3.bg.a	64	2
672.3.bh	\(\chi_{672}(481, \cdot)\)	672.3.bh.a	16	2
		672.3.bh.b	16
		672.3.bh.c	16
		672.3.bh.d	16
672.3.bm	\(\chi_{672}(47, \cdot)\)	n/a	120	2
672.3.bn	\(\chi_{672}(65, \cdot)\)	n/a	128	2
672.3.bp	\(\chi_{672}(43, \cdot)\)	n/a	384	4
672.3.br	\(\chi_{672}(83, \cdot)\)	n/a	1008	4
672.3.bt	\(\chi_{672}(13, \cdot)\)	n/a	512	4
672.3.bv	\(\chi_{672}(29, \cdot)\)	n/a	768	4
672.3.bx	\(\chi_{672}(151, \cdot)\)	None	0	4
672.3.bz	\(\chi_{672}(215, \cdot)\)	None	0	4
672.3.cb	\(\chi_{672}(137, \cdot)\)	None	0	4
672.3.cd	\(\chi_{672}(73, \cdot)\)	None	0	4
672.3.ce	\(\chi_{672}(53, \cdot)\)	n/a	2016	8
672.3.cg	\(\chi_{672}(61, \cdot)\)	n/a	1024	8
672.3.ci	\(\chi_{672}(59, \cdot)\)	n/a	2016	8
672.3.ck	\(\chi_{672}(67, \cdot)\)	n/a	1024	8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(672))\) into lower level spaces

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