Space of modular forms of level 576 and weight 7

• Label: 576.7
• Level: 576
• Weight: 7
• Dimension: 24525
• Nonzero newspaces: 16
• Sturm bound: 129024
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(129024\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(576))\).

	Total	New	Old
Modular forms	55872	24723	31149
Cusp forms	54720	24525	30195
Eisenstein series	1152	198	954

Trace form

24525 * 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 - 1378 * q^11 - 32 * q^12 + 5016 * q^13 - 24 * q^14 - 24 * q^15 - 24 * q^16 - 9818 * q^17 - 32 * q^18 - 3990 * q^19 - 24 * q^20 - 32 * q^21 - 63744 * q^22 + 13096 * q^23 - 32 * q^24 + 25529 * q^25 - 10624 * q^26 - 24 * q^27 - 171072 * q^28 - 66424 * q^29 - 32 * q^30 - 28 * q^31 + 117776 * q^32 - 2940 * q^33 + 278976 * q^34 - 12600 * q^35 - 32 * q^36 + 173448 * q^37 - 200224 * q^38 + 254376 * q^39 - 575664 * q^40 - 342430 * q^41 - 32 * q^42 - 513090 * q^43 + 480976 * q^44 - 515648 * q^45 - 72 * q^46 - 12 * q^47 - 32 * q^48 + 500069 * q^49 + 705408 * q^50 + 767176 * q^51 - 1275144 * q^52 + 903288 * q^53 - 32 * q^54 + 232652 * q^55 + 326512 * q^56 - 977000 * q^57 + 1770096 * q^58 - 3427138 * q^59 - 32 * q^60 + 589656 * q^61 + 543192 * q^62 + 470572 * q^63 - 1155240 * q^64 + 481188 * q^65 - 32 * q^66 + 3141966 * q^67 - 1847304 * q^68 + 5800 * q^69 - 2272056 * q^70 + 801012 * q^71 - 32 * q^72 + 135846 * q^73 + 2924128 * q^74 + 65392 * q^75 + 4565160 * q^76 + 2207172 * q^77 + 9469648 * q^78 + 3443692 * q^79 - 10442352 * q^80 - 4842936 * q^81 - 20900952 * q^82 - 5860498 * q^83 - 11943040 * q^84 - 3777288 * q^85 + 2485056 * q^86 + 2029864 * q^87 + 14086776 * q^88 + 14397826 * q^89 + 22931968 * q^90 + 7099148 * q^91 + 30316224 * q^92 + 4699168 * q^93 + 7526280 * q^94 + 12 * q^95 - 7416112 * q^96 - 13434786 * q^97 - 31046784 * q^98 - 5970712 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.7.b	\(\chi_{576}(415, \cdot)\)	576.7.b.a	4	1
		576.7.b.b	4
		576.7.b.c	4
		576.7.b.d	8
		576.7.b.e	8
		576.7.b.f	8
		576.7.b.g	8
		576.7.b.h	16
576.7.e	\(\chi_{576}(449, \cdot)\)	576.7.e.a	2	1
		576.7.e.b	2
		576.7.e.c	2
		576.7.e.d	2
		576.7.e.e	2
		576.7.e.f	2
		576.7.e.g	2
		576.7.e.h	2
		576.7.e.i	2
		576.7.e.j	2
		576.7.e.k	2
		576.7.e.l	2
		576.7.e.m	4
		576.7.e.n	4
		576.7.e.o	4
		576.7.e.p	4
		576.7.e.q	4
		576.7.e.r	4
576.7.g	\(\chi_{576}(127, \cdot)\)	576.7.g.a	1	1
		576.7.g.b	1
		576.7.g.c	1
		576.7.g.d	2
		576.7.g.e	2
		576.7.g.f	2
		576.7.g.g	2
		576.7.g.h	2
		576.7.g.i	2
		576.7.g.j	2
		576.7.g.k	4
		576.7.g.l	4
		576.7.g.m	4
		576.7.g.n	4
		576.7.g.o	6
		576.7.g.p	6
		576.7.g.q	6
		576.7.g.r	8
576.7.h	\(\chi_{576}(161, \cdot)\)	576.7.h.a	16	1
		576.7.h.b	32
576.7.j	\(\chi_{576}(17, \cdot)\)	576.7.j.a	96	2
576.7.m	\(\chi_{576}(271, \cdot)\)	n/a	118	2
576.7.n	\(\chi_{576}(353, \cdot)\)	n/a	288	2
576.7.o	\(\chi_{576}(319, \cdot)\)	n/a	284	2
576.7.q	\(\chi_{576}(65, \cdot)\)	n/a	284	2
576.7.t	\(\chi_{576}(31, \cdot)\)	n/a	288	2
576.7.u	\(\chi_{576}(55, \cdot)\)	None	0	4
576.7.x	\(\chi_{576}(89, \cdot)\)	None	0	4
576.7.z	\(\chi_{576}(79, \cdot)\)	n/a	568	4
576.7.ba	\(\chi_{576}(113, \cdot)\)	n/a	568	4
576.7.bc	\(\chi_{576}(53, \cdot)\)	n/a	1536	8
576.7.bf	\(\chi_{576}(19, \cdot)\)	n/a	1912	8
576.7.bh	\(\chi_{576}(7, \cdot)\)	None	0	8
576.7.bi	\(\chi_{576}(41, \cdot)\)	None	0	8
576.7.bk	\(\chi_{576}(43, \cdot)\)	n/a	9184	16
576.7.bn	\(\chi_{576}(5, \cdot)\)	n/a	9184	16

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

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