Space of modular forms of level 576 and weight 3

• Label: 576.3
• Level: 576
• Weight: 3
• Dimension: 8109
• Nonzero newspaces: 16
• Sturm bound: 55296
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(55296\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(576))\).

	Total	New	Old
Modular forms	19008	8307	10701
Cusp forms	17856	8109	9747
Eisenstein series	1152	198	954

Trace form

8109 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 32 * q^6 - 16 * q^7 - 24 * q^8 - 40 * q^9 - 72 * q^10 - 2 * q^11 - 32 * q^12 - 8 * q^13 - 24 * q^14 - 24 * q^15 - 24 * q^16 - 58 * q^17 - 32 * q^18 - 86 * q^19 - 24 * q^20 - 32 * q^21 - 96 * q^22 - 88 * q^23 - 32 * q^24 - 151 * q^25 - 224 * q^26 - 24 * q^27 - 192 * q^28 - 56 * q^29 - 32 * q^30 - 28 * q^31 + 16 * q^32 - 60 * q^33 + 96 * q^34 - 120 * q^35 - 32 * q^36 - 216 * q^37 + 256 * q^38 - 216 * q^39 + 336 * q^40 - 158 * q^41 - 32 * q^42 - 162 * q^43 + 80 * q^44 - 128 * q^45 - 72 * q^46 - 12 * q^47 - 32 * q^48 + 5 * q^49 + 288 * q^50 + 136 * q^51 + 504 * q^52 + 408 * q^53 - 32 * q^54 - 308 * q^55 + 368 * q^56 + 280 * q^57 + 336 * q^58 + 94 * q^59 - 32 * q^60 + 312 * q^61 + 120 * q^62 + 172 * q^63 - 168 * q^64 + 228 * q^65 - 32 * q^66 + 526 * q^67 - 264 * q^68 + 40 * q^69 - 696 * q^70 + 756 * q^71 - 32 * q^72 + 166 * q^73 - 640 * q^74 + 112 * q^75 - 856 * q^76 + 612 * q^77 + 784 * q^78 + 1004 * q^79 + 2448 * q^80 + 840 * q^81 + 3048 * q^82 + 622 * q^83 + 2432 * q^84 + 792 * q^85 + 2784 * q^86 + 424 * q^87 + 1656 * q^88 + 962 * q^89 + 1408 * q^90 + 140 * q^91 + 1344 * q^92 + 160 * q^93 + 264 * q^94 + 12 * q^95 - 304 * q^96 - 322 * q^97 - 1248 * q^98 - 280 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.3.b	\(\chi_{576}(415, \cdot)\)	576.3.b.a	4	1
		576.3.b.b	4
		576.3.b.c	4
		576.3.b.d	4
		576.3.b.e	4
576.3.e	\(\chi_{576}(449, \cdot)\)	576.3.e.a	2	1
		576.3.e.b	2
		576.3.e.c	2
		576.3.e.d	2
		576.3.e.e	2
		576.3.e.f	2
		576.3.e.g	2
		576.3.e.h	2
576.3.g	\(\chi_{576}(127, \cdot)\)	576.3.g.a	1	1
		576.3.g.b	1
		576.3.g.c	1
		576.3.g.d	2
		576.3.g.e	2
		576.3.g.f	2
		576.3.g.g	2
		576.3.g.h	2
		576.3.g.i	2
		576.3.g.j	4
576.3.h	\(\chi_{576}(161, \cdot)\)	576.3.h.a	8	1
		576.3.h.b	8
576.3.j	\(\chi_{576}(17, \cdot)\)	576.3.j.a	32	2
576.3.m	\(\chi_{576}(271, \cdot)\)	576.3.m.a	6	2
		576.3.m.b	16
		576.3.m.c	16
576.3.n	\(\chi_{576}(353, \cdot)\)	576.3.n.a	8	2
		576.3.n.b	24
		576.3.n.c	32
		576.3.n.d	32
576.3.o	\(\chi_{576}(319, \cdot)\)	576.3.o.a	2	2
		576.3.o.b	2
		576.3.o.c	4
		576.3.o.d	8
		576.3.o.e	8
		576.3.o.f	8
		576.3.o.g	16
		576.3.o.h	20
		576.3.o.i	24
576.3.q	\(\chi_{576}(65, \cdot)\)	576.3.q.a	2	2
		576.3.q.b	2
		576.3.q.c	4
		576.3.q.d	4
		576.3.q.e	4
		576.3.q.f	4
		576.3.q.g	4
		576.3.q.h	4
		576.3.q.i	8
		576.3.q.j	8
		576.3.q.k	24
		576.3.q.l	24
576.3.t	\(\chi_{576}(31, \cdot)\)	576.3.t.a	32	2
		576.3.t.b	32
		576.3.t.c	32
576.3.u	\(\chi_{576}(55, \cdot)\)	None	0	4
576.3.x	\(\chi_{576}(89, \cdot)\)	None	0	4
576.3.z	\(\chi_{576}(79, \cdot)\)	n/a	184	4
576.3.ba	\(\chi_{576}(113, \cdot)\)	n/a	184	4
576.3.bc	\(\chi_{576}(53, \cdot)\)	n/a	512	8
576.3.bf	\(\chi_{576}(19, \cdot)\)	n/a	632	8
576.3.bh	\(\chi_{576}(7, \cdot)\)	None	0	8
576.3.bi	\(\chi_{576}(41, \cdot)\)	None	0	8
576.3.bk	\(\chi_{576}(43, \cdot)\)	n/a	3040	16
576.3.bn	\(\chi_{576}(5, \cdot)\)	n/a	3040	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

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