Space of modular forms of level 1728 and weight 4

• Label: 1728.4
• Level: 1728
• Weight: 4
• Dimension: 110240
• Nonzero newspaces: 24
• Sturm bound: 663552
• Trace bound: 52

Defining parameters

Level:	\( N \)	=	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(663552\)
Trace bound:			\(52\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1728))\).

	Total	New	Old
Modular forms	250992	110944	140048
Cusp forms	246672	110240	136432
Eisenstein series	4320	704	3616

Trace form

110240 * 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 - 52 * 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 - 548 * q^35 - 96 * q^36 - 1120 * q^37 - 64 * q^38 - 72 * q^39 - 112 * q^40 + 80 * q^41 - 96 * q^42 + 780 * q^43 - 64 * q^44 - 96 * q^45 - 112 * q^46 + 1836 * q^47 - 96 * q^48 + 1244 * q^49 - 64 * q^50 - 72 * q^51 - 112 * q^52 + 752 * q^53 - 96 * q^54 - 480 * q^55 - 64 * q^56 - 120 * q^57 - 112 * q^58 - 2088 * q^59 - 96 * q^60 - 2272 * q^61 + 64 * q^62 - 72 * q^63 - 112 * q^64 - 676 * q^65 - 96 * q^66 - 84 * q^67 - 64 * q^68 - 96 * q^69 - 112 * q^70 - 28 * q^71 - 96 * q^72 - 140 * q^73 - 64 * q^74 - 72 * q^75 - 112 * q^76 + 2680 * q^77 - 96 * q^78 + 2748 * q^79 + 18496 * q^80 - 168 * q^81 + 13664 * q^82 + 2392 * q^83 - 96 * q^84 + 848 * q^85 - 1104 * q^86 - 72 * q^87 - 6352 * q^88 - 6864 * q^89 - 96 * q^90 - 3684 * q^91 - 25296 * q^92 - 96 * q^93 - 17968 * q^94 - 6108 * q^95 - 96 * q^96 - 11988 * q^97 - 24272 * q^98 - 72 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1728))\)

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
1728.4.a	\(\chi_{1728}(1, \cdot)\)	1728.4.a.a	1	1
		1728.4.a.b	1
		1728.4.a.c	1
		1728.4.a.d	1
		1728.4.a.e	1
		1728.4.a.f	1
		1728.4.a.g	1
		1728.4.a.h	1
		1728.4.a.i	1
		1728.4.a.j	1
		1728.4.a.k	1
		1728.4.a.l	1
		1728.4.a.m	1
		1728.4.a.n	1
		1728.4.a.o	1
		1728.4.a.p	1
		1728.4.a.q	1
		1728.4.a.r	1
		1728.4.a.s	1
		1728.4.a.t	1
		1728.4.a.u	1
		1728.4.a.v	1
		1728.4.a.w	1
		1728.4.a.x	1
		1728.4.a.y	1
		1728.4.a.z	1
		1728.4.a.ba	1
		1728.4.a.bb	1
		1728.4.a.bc	1
		1728.4.a.bd	1
		1728.4.a.be	1
		1728.4.a.bf	1
		1728.4.a.bg	2
		1728.4.a.bh	2
		1728.4.a.bi	2
		1728.4.a.bj	2
		1728.4.a.bk	2
		1728.4.a.bl	2
		1728.4.a.bm	2
		1728.4.a.bn	2
		1728.4.a.bo	2
		1728.4.a.bp	2
		1728.4.a.bq	2
		1728.4.a.br	2
		1728.4.a.bs	2
		1728.4.a.bt	2
		1728.4.a.bu	3
		1728.4.a.bv	3
		1728.4.a.bw	3
		1728.4.a.bx	3
		1728.4.a.by	3
		1728.4.a.bz	3
		1728.4.a.ca	3
		1728.4.a.cb	3
		1728.4.a.cc	3
		1728.4.a.cd	3
		1728.4.a.ce	3
		1728.4.a.cf	3
1728.4.c	\(\chi_{1728}(1727, \cdot)\)	1728.4.c.a	2	1
		1728.4.c.b	2
		1728.4.c.c	2
		1728.4.c.d	2
		1728.4.c.e	4
		1728.4.c.f	4
		1728.4.c.g	4
		1728.4.c.h	4
		1728.4.c.i	12
		1728.4.c.j	12
		1728.4.c.k	24
		1728.4.c.l	24
1728.4.d	\(\chi_{1728}(865, \cdot)\)	1728.4.d.a	4	1
		1728.4.d.b	4
		1728.4.d.c	4
		1728.4.d.d	4
		1728.4.d.e	8
		1728.4.d.f	8
		1728.4.d.g	8
		1728.4.d.h	8
		1728.4.d.i	16
		1728.4.d.j	16
		1728.4.d.k	16
1728.4.f	\(\chi_{1728}(863, \cdot)\)	1728.4.f.a	4	1
		1728.4.f.b	4
		1728.4.f.c	8
		1728.4.f.d	8
		1728.4.f.e	8
		1728.4.f.f	8
		1728.4.f.g	8
		1728.4.f.h	16
		1728.4.f.i	16
		1728.4.f.j	16
1728.4.i	\(\chi_{1728}(577, \cdot)\)	n/a	140	2
1728.4.k	\(\chi_{1728}(433, \cdot)\)	n/a	192	2
1728.4.l	\(\chi_{1728}(431, \cdot)\)	n/a	192	2
1728.4.p	\(\chi_{1728}(287, \cdot)\)	n/a	144	2
1728.4.r	\(\chi_{1728}(289, \cdot)\)	n/a	144	2
1728.4.s	\(\chi_{1728}(575, \cdot)\)	n/a	140	2
1728.4.v	\(\chi_{1728}(217, \cdot)\)	None	0	4
1728.4.w	\(\chi_{1728}(215, \cdot)\)	None	0	4
1728.4.y	\(\chi_{1728}(193, \cdot)\)	n/a	1284	6
1728.4.z	\(\chi_{1728}(143, \cdot)\)	n/a	280	4
1728.4.bc	\(\chi_{1728}(145, \cdot)\)	n/a	280	4
1728.4.be	\(\chi_{1728}(109, \cdot)\)	n/a	3072	8
1728.4.bf	\(\chi_{1728}(107, \cdot)\)	n/a	3072	8
1728.4.bj	\(\chi_{1728}(97, \cdot)\)	n/a	1296	6
1728.4.bl	\(\chi_{1728}(95, \cdot)\)	n/a	1296	6
1728.4.bm	\(\chi_{1728}(191, \cdot)\)	n/a	1284	6
1728.4.bo	\(\chi_{1728}(73, \cdot)\)	None	0	8
1728.4.br	\(\chi_{1728}(71, \cdot)\)	None	0	8
1728.4.bs	\(\chi_{1728}(49, \cdot)\)	n/a	2568	12
1728.4.bv	\(\chi_{1728}(47, \cdot)\)	n/a	2568	12
1728.4.bx	\(\chi_{1728}(35, \cdot)\)	n/a	4576	16
1728.4.by	\(\chi_{1728}(37, \cdot)\)	n/a	4576	16
1728.4.cb	\(\chi_{1728}(23, \cdot)\)	None	0	24
1728.4.cc	\(\chi_{1728}(25, \cdot)\)	None	0	24
1728.4.ce	\(\chi_{1728}(13, \cdot)\)	n/a	41376	48
1728.4.ch	\(\chi_{1728}(11, \cdot)\)	n/a	41376	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1728))\) into lower level spaces

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