Space of modular forms of level 576 and weight 8

• Label: 576.8
• Level: 576
• Weight: 8
• Dimension: 28629
• Nonzero newspaces: 16
• Sturm bound: 147456
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(147456\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(576))\).

	Total	New	Old
Modular forms	65088	28827	36261
Cusp forms	63936	28629	35307
Eisenstein series	1152	198	954

Trace form

28629 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 32 * q^6 - 20 * q^7 - 24 * q^8 - 40 * q^9 - 72 * q^10 - 1222 * q^11 - 32 * q^12 - 7088 * q^13 - 24 * q^14 - 24 * q^15 - 24 * q^16 - 5858 * q^17 - 32 * q^18 - 60638 * q^19 - 24 * q^20 - 32 * q^21 + 274432 * q^22 - 12 * q^23 - 32 * q^24 - 13659 * q^25 + 727936 * q^26 - 24 * q^27 + 390848 * q^28 - 103400 * q^29 - 32 * q^30 - 357500 * q^31 - 1071344 * q^32 + 8724 * q^33 + 403136 * q^34 + 876984 * q^35 - 32 * q^36 - 1070992 * q^37 + 1244896 * q^38 - 283968 * q^39 - 2686384 * q^40 + 1842082 * q^41 - 32 * q^42 + 2441618 * q^43 + 3370448 * q^44 - 2210960 * q^45 - 72 * q^46 - 6229404 * q^47 - 32 * q^48 - 2242787 * q^49 - 2317440 * q^50 + 2234416 * q^51 + 10204920 * q^52 + 11597952 * q^53 - 32 * q^54 + 16763976 * q^55 - 10737296 * q^56 - 2745416 * q^57 - 10358160 * q^58 - 7251694 * q^59 - 32 * q^60 - 922320 * q^61 + 10344408 * q^62 + 3294148 * q^63 + 22837080 * q^64 - 291580 * q^65 - 32 * q^66 + 9445798 * q^67 - 8750088 * q^68 - 17528 * q^69 - 35990328 * q^70 + 24697384 * q^71 - 32 * q^72 - 2836570 * q^73 + 4214368 * q^74 - 303776 * q^75 + 38942888 * q^76 - 2194548 * q^77 - 78695216 * q^78 + 9598892 * q^79 + 108869520 * q^80 + 54057480 * q^81 + 147943848 * q^82 + 14600542 * q^83 - 34113664 * q^84 - 55819968 * q^85 - 208606656 * q^86 - 40789136 * q^87 - 157553544 * q^88 - 100935502 * q^89 - 63468032 * q^90 + 4226276 * q^91 + 163322304 * q^92 + 57999040 * q^93 + 224074632 * q^94 + 114644568 * q^95 + 225737936 * q^96 + 144734470 * q^97 + 188307072 * q^98 + 9729704 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.8.a	\(\chi_{576}(1, \cdot)\)	576.8.a.a	1	1
		576.8.a.b	1
		576.8.a.c	1
		576.8.a.d	1
		576.8.a.e	1
		576.8.a.f	1
		576.8.a.g	1
		576.8.a.h	1
		576.8.a.i	1
		576.8.a.j	1
		576.8.a.k	1
		576.8.a.l	1
		576.8.a.m	1
		576.8.a.n	1
		576.8.a.o	1
		576.8.a.p	1
		576.8.a.q	1
		576.8.a.r	1
		576.8.a.s	1
		576.8.a.t	1
		576.8.a.u	1
		576.8.a.v	1
		576.8.a.w	1
		576.8.a.x	1
		576.8.a.y	1
		576.8.a.z	1
		576.8.a.ba	1
		576.8.a.bb	2
		576.8.a.bc	2
		576.8.a.bd	2
		576.8.a.be	2
		576.8.a.bf	2
		576.8.a.bg	2
		576.8.a.bh	2
		576.8.a.bi	2
		576.8.a.bj	2
		576.8.a.bk	2
		576.8.a.bl	2
		576.8.a.bm	2
		576.8.a.bn	2
		576.8.a.bo	2
		576.8.a.bp	2
		576.8.a.bq	2
		576.8.a.br	2
		576.8.a.bs	4
		576.8.a.bt	4
576.8.c	\(\chi_{576}(575, \cdot)\)	576.8.c.a	2	1
		576.8.c.b	2
		576.8.c.c	4
		576.8.c.d	8
		576.8.c.e	12
		576.8.c.f	12
		576.8.c.g	16
576.8.d	\(\chi_{576}(289, \cdot)\)	576.8.d.a	2	1
		576.8.d.b	4
		576.8.d.c	4
		576.8.d.d	4
		576.8.d.e	4
		576.8.d.f	8
		576.8.d.g	8
		576.8.d.h	8
		576.8.d.i	12
		576.8.d.j	16
576.8.f	\(\chi_{576}(287, \cdot)\)	576.8.f.a	16	1
		576.8.f.b	40
576.8.i	\(\chi_{576}(193, \cdot)\)	n/a	332	2
576.8.k	\(\chi_{576}(145, \cdot)\)	n/a	138	2
576.8.l	\(\chi_{576}(143, \cdot)\)	n/a	112	2
576.8.p	\(\chi_{576}(95, \cdot)\)	n/a	336	2
576.8.r	\(\chi_{576}(97, \cdot)\)	n/a	336	2
576.8.s	\(\chi_{576}(191, \cdot)\)	n/a	332	2
576.8.v	\(\chi_{576}(73, \cdot)\)	None	0	4
576.8.w	\(\chi_{576}(71, \cdot)\)	None	0	4
576.8.y	\(\chi_{576}(47, \cdot)\)	n/a	664	4
576.8.bb	\(\chi_{576}(49, \cdot)\)	n/a	664	4
576.8.bd	\(\chi_{576}(37, \cdot)\)	n/a	2232	8
576.8.be	\(\chi_{576}(35, \cdot)\)	n/a	1792	8
576.8.bg	\(\chi_{576}(25, \cdot)\)	None	0	8
576.8.bj	\(\chi_{576}(23, \cdot)\)	None	0	8
576.8.bl	\(\chi_{576}(11, \cdot)\)	n/a	10720	16
576.8.bm	\(\chi_{576}(13, \cdot)\)	n/a	10720	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

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