Space of modular forms of level 576 and weight 2

• Label: 576.2
• Level: 576
• Weight: 2
• Dimension: 4005
• Nonzero newspaces: 16
• Newform subspaces: 63
• Sturm bound: 36864
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 63 \)
Sturm bound:			\(36864\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(576))\).

	Total	New	Old
Modular forms	9792	4203	5589
Cusp forms	8641	4005	4636
Eisenstein series	1151	198	953

Trace form

4005 * 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 - 22 * q^11 - 32 * q^12 - 32 * q^13 - 24 * q^14 - 24 * q^15 - 24 * q^16 - 50 * q^17 - 32 * q^18 - 62 * q^19 - 24 * q^20 - 32 * q^21 - 16 * q^22 - 12 * q^23 - 32 * q^24 - 19 * q^25 + 16 * q^26 - 24 * q^27 - 32 * q^28 - 8 * q^29 - 32 * q^30 + 4 * q^31 + 16 * q^32 - 12 * q^33 + 16 * q^34 + 24 * q^35 - 32 * q^36 - 32 * q^37 + 16 * q^38 + 16 * q^40 + 34 * q^41 - 32 * q^42 + 34 * q^43 - 16 * q^44 + 16 * q^45 - 72 * q^46 + 36 * q^47 - 32 * q^48 + 13 * q^49 - 48 * q^50 + 16 * q^51 - 72 * q^52 + 48 * q^53 - 32 * q^54 + 72 * q^55 - 80 * q^56 - 8 * q^57 - 96 * q^58 + 98 * q^59 - 32 * q^60 - 120 * q^62 + 4 * q^63 - 168 * q^64 - 28 * q^65 - 32 * q^66 + 70 * q^67 - 72 * q^68 - 56 * q^69 - 120 * q^70 + 40 * q^71 - 32 * q^72 - 90 * q^73 - 80 * q^74 - 32 * q^75 - 88 * q^76 - 132 * q^77 - 80 * q^78 - 20 * q^79 - 240 * q^80 - 120 * q^81 - 312 * q^82 - 98 * q^83 - 256 * q^84 - 144 * q^85 - 336 * q^86 - 80 * q^87 - 264 * q^88 - 238 * q^89 - 320 * q^90 - 156 * q^91 - 480 * q^92 - 128 * q^93 - 312 * q^94 - 168 * q^95 - 304 * q^96 - 234 * q^97 - 432 * q^98 - 88 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.2.a	\(\chi_{576}(1, \cdot)\)	576.2.a.a	1	1
		576.2.a.b	1
		576.2.a.c	1
		576.2.a.d	1
		576.2.a.e	1
		576.2.a.f	1
		576.2.a.g	1
		576.2.a.h	1
		576.2.a.i	1
576.2.c	\(\chi_{576}(575, \cdot)\)	576.2.c.a	2	1
		576.2.c.b	2
		576.2.c.c	4
576.2.d	\(\chi_{576}(289, \cdot)\)	576.2.d.a	2	1
		576.2.d.b	4
		576.2.d.c	4
576.2.f	\(\chi_{576}(287, \cdot)\)	576.2.f.a	8	1
576.2.i	\(\chi_{576}(193, \cdot)\)	576.2.i.a	2	2
		576.2.i.b	2
		576.2.i.c	2
		576.2.i.d	2
		576.2.i.e	2
		576.2.i.f	2
		576.2.i.g	2
		576.2.i.h	2
		576.2.i.i	4
		576.2.i.j	4
		576.2.i.k	4
		576.2.i.l	4
		576.2.i.m	4
		576.2.i.n	8
576.2.k	\(\chi_{576}(145, \cdot)\)	576.2.k.a	2	2
		576.2.k.b	8
		576.2.k.c	8
576.2.l	\(\chi_{576}(143, \cdot)\)	576.2.l.a	16	2
576.2.p	\(\chi_{576}(95, \cdot)\)	576.2.p.a	16	2
		576.2.p.b	16
		576.2.p.c	16
576.2.r	\(\chi_{576}(97, \cdot)\)	576.2.r.a	4	2
		576.2.r.b	4
		576.2.r.c	8
		576.2.r.d	8
		576.2.r.e	12
		576.2.r.f	12
576.2.s	\(\chi_{576}(191, \cdot)\)	576.2.s.a	2	2
		576.2.s.b	2
		576.2.s.c	2
		576.2.s.d	2
		576.2.s.e	4
		576.2.s.f	8
		576.2.s.g	24
576.2.v	\(\chi_{576}(73, \cdot)\)	None	0	4
576.2.w	\(\chi_{576}(71, \cdot)\)	None	0	4
576.2.y	\(\chi_{576}(47, \cdot)\)	576.2.y.a	88	4
576.2.bb	\(\chi_{576}(49, \cdot)\)	576.2.bb.a	4	4
		576.2.bb.b	4
		576.2.bb.c	4
		576.2.bb.d	4
		576.2.bb.e	72
576.2.bd	\(\chi_{576}(37, \cdot)\)	576.2.bd.a	56	8
		576.2.bd.b	128
		576.2.bd.c	128
576.2.be	\(\chi_{576}(35, \cdot)\)	576.2.be.a	128	8
		576.2.be.b	128
576.2.bg	\(\chi_{576}(25, \cdot)\)	None	0	8
576.2.bj	\(\chi_{576}(23, \cdot)\)	None	0	8
576.2.bl	\(\chi_{576}(11, \cdot)\)	576.2.bl.a	1504	16
576.2.bm	\(\chi_{576}(13, \cdot)\)	576.2.bm.a	1504	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

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