Space of modular forms of level 576 and weight 6

• Label: 576.6
• Level: 576
• Weight: 6
• Dimension: 20421
• Nonzero newspaces: 16
• Sturm bound: 110592
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(110592\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(576))\).

	Total	New	Old
Modular forms	46656	20619	26037
Cusp forms	45504	20421	25083
Eisenstein series	1152	198	954

Trace form

20421 * 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 + 586 * q^11 - 32 * q^12 - 256 * q^13 - 24 * q^14 - 24 * q^15 - 24 * q^16 - 850 * q^17 - 32 * q^18 + 2306 * q^19 - 24 * q^20 - 32 * q^21 + 13568 * q^22 - 12 * q^23 - 32 * q^24 - 15619 * q^25 - 25984 * q^26 - 24 * q^27 + 4288 * q^28 + 8120 * q^29 - 32 * q^30 + 11524 * q^31 + 37136 * q^32 + 948 * q^33 + 12736 * q^34 + 16344 * q^35 - 32 * q^36 - 14912 * q^37 - 69664 * q^38 - 44928 * q^39 - 62384 * q^40 - 79582 * q^41 - 32 * q^42 + 17986 * q^43 + 65488 * q^44 + 72016 * q^45 - 72 * q^46 + 132516 * q^47 - 32 * q^48 + 104557 * q^49 - 137088 * q^50 + 16336 * q^51 + 73464 * q^52 - 116592 * q^53 - 32 * q^54 - 440248 * q^55 + 150896 * q^56 - 123272 * q^57 + 25968 * q^58 + 26626 * q^59 - 32 * q^60 + 150432 * q^61 - 176424 * q^62 + 67204 * q^63 - 374952 * q^64 + 38692 * q^65 - 32 * q^66 + 197510 * q^67 - 7176 * q^68 - 1976 * q^69 + 286920 * q^70 - 287704 * q^71 - 32 * q^72 - 85082 * q^73 + 377696 * q^74 - 11552 * q^75 + 268456 * q^76 - 322212 * q^77 - 1055024 * q^78 + 52844 * q^79 - 1074288 * q^80 + 169608 * q^81 + 1509288 * q^82 + 430622 * q^83 + 1970048 * q^84 + 810192 * q^85 + 2165568 * q^86 + 282160 * q^87 + 669816 * q^88 + 216274 * q^89 - 568832 * q^90 - 169116 * q^91 - 2763840 * q^92 - 724736 * q^93 - 2463864 * q^94 - 904872 * q^95 - 2428720 * q^96 - 1599562 * q^97 - 2871936 * q^98 - 339544 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(576))\)

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
576.6.a	\(\chi_{576}(1, \cdot)\)	576.6.a.a	1	1
		576.6.a.b	1
		576.6.a.c	1
		576.6.a.d	1
		576.6.a.e	1
		576.6.a.f	1
		576.6.a.g	1
		576.6.a.h	1
		576.6.a.i	1
		576.6.a.j	1
		576.6.a.k	1
		576.6.a.l	1
		576.6.a.m	1
		576.6.a.n	1
		576.6.a.o	1
		576.6.a.p	1
		576.6.a.q	1
		576.6.a.r	1
		576.6.a.s	1
		576.6.a.t	1
		576.6.a.u	1
		576.6.a.v	1
		576.6.a.w	1
		576.6.a.x	1
		576.6.a.y	1
		576.6.a.z	1
		576.6.a.ba	1
		576.6.a.bb	1
		576.6.a.bc	1
		576.6.a.bd	1
		576.6.a.be	1
		576.6.a.bf	1
		576.6.a.bg	1
		576.6.a.bh	1
		576.6.a.bi	1
		576.6.a.bj	2
		576.6.a.bk	2
		576.6.a.bl	2
		576.6.a.bm	2
		576.6.a.bn	2
		576.6.a.bo	2
		576.6.a.bp	2
576.6.c	\(\chi_{576}(575, \cdot)\)	576.6.c.a	2	1
		576.6.c.b	2
		576.6.c.c	8
		576.6.c.d	8
		576.6.c.e	8
		576.6.c.f	12
576.6.d	\(\chi_{576}(289, \cdot)\)	576.6.d.a	2	1
		576.6.d.b	4
		576.6.d.c	4
		576.6.d.d	4
		576.6.d.e	4
		576.6.d.f	8
		576.6.d.g	8
		576.6.d.h	8
		576.6.d.i	8
576.6.f	\(\chi_{576}(287, \cdot)\)	576.6.f.a	8	1
		576.6.f.b	8
		576.6.f.c	24
576.6.i	\(\chi_{576}(193, \cdot)\)	n/a	236	2
576.6.k	\(\chi_{576}(145, \cdot)\)	576.6.k.a	18	2
		576.6.k.b	40
		576.6.k.c	40
576.6.l	\(\chi_{576}(143, \cdot)\)	576.6.l.a	80	2
576.6.p	\(\chi_{576}(95, \cdot)\)	n/a	240	2
576.6.r	\(\chi_{576}(97, \cdot)\)	n/a	240	2
576.6.s	\(\chi_{576}(191, \cdot)\)	n/a	236	2
576.6.v	\(\chi_{576}(73, \cdot)\)	None	0	4
576.6.w	\(\chi_{576}(71, \cdot)\)	None	0	4
576.6.y	\(\chi_{576}(47, \cdot)\)	n/a	472	4
576.6.bb	\(\chi_{576}(49, \cdot)\)	n/a	472	4
576.6.bd	\(\chi_{576}(37, \cdot)\)	n/a	1592	8
576.6.be	\(\chi_{576}(35, \cdot)\)	n/a	1280	8
576.6.bg	\(\chi_{576}(25, \cdot)\)	None	0	8
576.6.bj	\(\chi_{576}(23, \cdot)\)	None	0	8
576.6.bl	\(\chi_{576}(11, \cdot)\)	n/a	7648	16
576.6.bm	\(\chi_{576}(13, \cdot)\)	n/a	7648	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces

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