Space of modular forms of level 1728 and weight 3

• Label: 1728.3
• Level: 1728
• Weight: 3
• Dimension: 73376
• Nonzero newspaces: 24
• Sturm bound: 497664
• Trace bound: 52

Defining parameters

Level:	\( N \)	=	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(497664\)
Trace bound:			\(52\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1728))\).

	Total	New	Old
Modular forms	168048	74080	93968
Cusp forms	163728	73376	90352
Eisenstein series	4320	704	3616

Trace form

73376 * q - 64 * q^2 - 72 * q^3 - 112 * q^4 - 64 * q^5 - 96 * q^6 - 84 * q^7 - 64 * q^8 - 120 * q^9 - 112 * q^10 - 48 * q^11 - 96 * q^12 - 112 * q^13 - 64 * q^14 - 72 * q^15 - 112 * q^16 - 112 * q^17 - 96 * q^18 - 84 * q^19 - 64 * q^20 - 96 * q^21 - 112 * q^22 - 44 * q^23 - 96 * q^24 - 140 * q^25 - 64 * q^26 - 72 * q^27 - 256 * q^28 - 64 * q^29 - 96 * q^30 - 84 * q^31 - 64 * q^32 - 72 * q^33 - 112 * q^34 + 52 * q^35 - 96 * q^36 + 48 * q^37 - 64 * q^38 - 72 * q^39 - 112 * q^40 + 112 * q^41 - 96 * q^42 + 44 * q^43 - 64 * q^44 - 96 * q^45 - 112 * q^46 - 52 * q^47 - 96 * q^48 - 260 * q^49 - 64 * q^50 - 72 * q^51 - 112 * q^52 - 352 * q^53 - 96 * q^54 - 448 * q^55 - 64 * q^56 - 120 * q^57 - 112 * q^58 - 336 * q^59 - 96 * q^60 - 336 * q^61 - 128 * q^62 - 72 * q^63 - 112 * q^64 - 276 * q^65 - 96 * q^66 - 84 * q^67 - 64 * q^68 - 96 * q^69 - 112 * q^70 - 68 * q^71 - 96 * q^72 - 140 * q^73 - 64 * q^74 - 72 * q^75 - 112 * q^76 - 456 * q^77 - 96 * q^78 - 340 * q^79 - 1984 * q^80 - 168 * q^81 - 2336 * q^82 - 528 * q^83 - 96 * q^84 - 752 * q^85 - 1936 * q^86 - 72 * q^87 - 1232 * q^88 - 848 * q^89 - 96 * q^90 - 276 * q^91 - 976 * q^92 - 96 * q^93 - 304 * q^94 - 68 * q^95 - 96 * q^96 + 172 * q^97 + 752 * q^98 - 72 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1728))\)

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
1728.3.b	\(\chi_{1728}(1567, \cdot)\)	1728.3.b.a	4	1
		1728.3.b.b	4
		1728.3.b.c	4
		1728.3.b.d	4
		1728.3.b.e	4
		1728.3.b.f	4
		1728.3.b.g	8
		1728.3.b.h	8
		1728.3.b.i	12
		1728.3.b.j	12
1728.3.e	\(\chi_{1728}(1025, \cdot)\)	1728.3.e.a	1	1
		1728.3.e.b	1
		1728.3.e.c	1
		1728.3.e.d	1
		1728.3.e.e	2
		1728.3.e.f	2
		1728.3.e.g	2
		1728.3.e.h	2
		1728.3.e.i	2
		1728.3.e.j	2
		1728.3.e.k	2
		1728.3.e.l	2
		1728.3.e.m	2
		1728.3.e.n	2
		1728.3.e.o	4
		1728.3.e.p	4
		1728.3.e.q	4
		1728.3.e.r	4
		1728.3.e.s	4
		1728.3.e.t	4
		1728.3.e.u	8
		1728.3.e.v	8
1728.3.g	\(\chi_{1728}(703, \cdot)\)	1728.3.g.a	2	1
		1728.3.g.b	2
		1728.3.g.c	2
		1728.3.g.d	2
		1728.3.g.e	2
		1728.3.g.f	2
		1728.3.g.g	4
		1728.3.g.h	4
		1728.3.g.i	4
		1728.3.g.j	8
		1728.3.g.k	8
		1728.3.g.l	8
		1728.3.g.m	8
		1728.3.g.n	8
1728.3.h	\(\chi_{1728}(161, \cdot)\)	1728.3.h.a	4	1
		1728.3.h.b	4
		1728.3.h.c	4
		1728.3.h.d	4
		1728.3.h.e	4
		1728.3.h.f	4
		1728.3.h.g	8
		1728.3.h.h	8
		1728.3.h.i	12
		1728.3.h.j	12
1728.3.j	\(\chi_{1728}(593, \cdot)\)	n/a	128	2
1728.3.m	\(\chi_{1728}(271, \cdot)\)	n/a	128	2
1728.3.n	\(\chi_{1728}(737, \cdot)\)	1728.3.n.a	8	2
		1728.3.n.b	24
		1728.3.n.c	32
		1728.3.n.d	32
1728.3.o	\(\chi_{1728}(127, \cdot)\)	1728.3.o.a	2	2
		1728.3.o.b	2
		1728.3.o.c	4
		1728.3.o.d	8
		1728.3.o.e	8
		1728.3.o.f	8
		1728.3.o.g	16
		1728.3.o.h	20
		1728.3.o.i	24
1728.3.q	\(\chi_{1728}(449, \cdot)\)	1728.3.q.a	2	2
		1728.3.q.b	2
		1728.3.q.c	4
		1728.3.q.d	4
		1728.3.q.e	4
		1728.3.q.f	4
		1728.3.q.g	4
		1728.3.q.h	4
		1728.3.q.i	8
		1728.3.q.j	8
		1728.3.q.k	24
		1728.3.q.l	24
1728.3.t	\(\chi_{1728}(415, \cdot)\)	1728.3.t.a	32	2
		1728.3.t.b	32
		1728.3.t.c	32
1728.3.u	\(\chi_{1728}(55, \cdot)\)	None	0	4
1728.3.x	\(\chi_{1728}(377, \cdot)\)	None	0	4
1728.3.ba	\(\chi_{1728}(559, \cdot)\)	n/a	184	4
1728.3.bb	\(\chi_{1728}(17, \cdot)\)	n/a	184	4
1728.3.bd	\(\chi_{1728}(53, \cdot)\)	n/a	2048	8
1728.3.bg	\(\chi_{1728}(163, \cdot)\)	n/a	2048	8
1728.3.bh	\(\chi_{1728}(31, \cdot)\)	n/a	864	6
1728.3.bi	\(\chi_{1728}(319, \cdot)\)	n/a	852	6
1728.3.bk	\(\chi_{1728}(65, \cdot)\)	n/a	852	6
1728.3.bn	\(\chi_{1728}(353, \cdot)\)	n/a	864	6
1728.3.bp	\(\chi_{1728}(199, \cdot)\)	None	0	8
1728.3.bq	\(\chi_{1728}(89, \cdot)\)	None	0	8
1728.3.bt	\(\chi_{1728}(79, \cdot)\)	n/a	1704	12
1728.3.bu	\(\chi_{1728}(113, \cdot)\)	n/a	1704	12
1728.3.bw	\(\chi_{1728}(19, \cdot)\)	n/a	3040	16
1728.3.bz	\(\chi_{1728}(125, \cdot)\)	n/a	3040	16
1728.3.ca	\(\chi_{1728}(41, \cdot)\)	None	0	24
1728.3.cd	\(\chi_{1728}(7, \cdot)\)	None	0	24
1728.3.cf	\(\chi_{1728}(5, \cdot)\)	n/a	27552	48
1728.3.cg	\(\chi_{1728}(43, \cdot)\)	n/a	27552	48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1728))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1728)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 21}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 2}\)