Space of modular forms of level 528 and weight 6

• Label: 528.6
• Level: 528
• Weight: 6
• Dimension: 15848
• Nonzero newspaces: 16
• Sturm bound: 92160
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(92160\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(528))\).

	Total	New	Old
Modular forms	38960	16012	22948
Cusp forms	37840	15848	21992
Eisenstein series	1120	164	956

Trace form

15848 * q - 29 * q^3 - 120 * q^4 - 76 * q^5 + 212 * q^6 + 306 * q^7 + 984 * q^8 - 947 * q^9 - 1768 * q^10 - 1812 * q^11 - 24 * q^12 + 434 * q^13 - 648 * q^14 + 4485 * q^15 - 8392 * q^16 - 404 * q^17 + 8780 * q^18 - 19390 * q^19 + 15200 * q^20 - 3964 * q^21 - 1248 * q^22 + 9328 * q^23 - 15596 * q^24 + 3900 * q^25 + 25960 * q^26 + 5995 * q^27 + 3800 * q^28 + 16708 * q^29 + 1460 * q^30 - 40702 * q^31 - 88320 * q^32 + 16143 * q^33 - 62304 * q^34 - 45588 * q^35 + 64716 * q^36 - 27798 * q^37 + 144176 * q^38 + 74633 * q^39 + 180808 * q^40 + 118156 * q^41 + 5908 * q^42 + 66548 * q^43 - 43768 * q^44 + 24934 * q^45 - 244008 * q^46 - 57732 * q^47 - 71252 * q^48 - 289640 * q^49 - 212424 * q^50 - 244695 * q^51 + 329720 * q^52 + 99996 * q^53 + 68100 * q^54 + 99070 * q^55 + 317184 * q^56 + 248175 * q^57 + 70728 * q^58 + 61064 * q^59 + 71868 * q^60 - 114254 * q^61 - 382200 * q^62 - 37599 * q^63 - 715944 * q^64 - 60552 * q^65 - 155232 * q^66 - 403356 * q^67 + 244672 * q^68 - 202386 * q^69 + 75664 * q^70 - 381764 * q^71 - 197956 * q^72 - 401686 * q^73 + 886192 * q^74 + 398687 * q^75 + 1810232 * q^76 + 1112336 * q^77 + 1087832 * q^78 + 897886 * q^79 + 55224 * q^80 + 997037 * q^81 - 145864 * q^82 - 26300 * q^83 - 1158388 * q^84 - 1175978 * q^85 - 1122144 * q^86 - 705016 * q^87 - 4197864 * q^88 - 909476 * q^89 - 332724 * q^90 - 1325910 * q^91 - 674976 * q^92 - 975993 * q^93 + 217000 * q^94 + 272652 * q^95 + 1529876 * q^96 + 1286922 * q^97 + 4029288 * q^98 + 385693 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(528))\)

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
528.6.a	\(\chi_{528}(1, \cdot)\)	528.6.a.a	1	1
		528.6.a.b	1
		528.6.a.c	1
		528.6.a.d	1
		528.6.a.e	1
		528.6.a.f	1
		528.6.a.g	1
		528.6.a.h	1
		528.6.a.i	1
		528.6.a.j	1
		528.6.a.k	2
		528.6.a.l	2
		528.6.a.m	2
		528.6.a.n	2
		528.6.a.o	2
		528.6.a.p	2
		528.6.a.q	2
		528.6.a.r	2
		528.6.a.s	2
		528.6.a.t	3
		528.6.a.u	3
		528.6.a.v	3
		528.6.a.w	3
		528.6.a.x	3
		528.6.a.y	3
		528.6.a.z	4
528.6.b	\(\chi_{528}(65, \cdot)\)	n/a	118	1
528.6.d	\(\chi_{528}(287, \cdot)\)	528.6.d.a	16	1
		528.6.d.b	16
		528.6.d.c	34
		528.6.d.d	34
528.6.f	\(\chi_{528}(265, \cdot)\)	None	0	1
528.6.h	\(\chi_{528}(439, \cdot)\)	None	0	1
528.6.k	\(\chi_{528}(23, \cdot)\)	None	0	1
528.6.m	\(\chi_{528}(329, \cdot)\)	None	0	1
528.6.o	\(\chi_{528}(175, \cdot)\)	528.6.o.a	20	1
		528.6.o.b	40
528.6.q	\(\chi_{528}(43, \cdot)\)	n/a	480	2
528.6.t	\(\chi_{528}(133, \cdot)\)	n/a	400	2
528.6.u	\(\chi_{528}(155, \cdot)\)	n/a	800	2
528.6.x	\(\chi_{528}(197, \cdot)\)	n/a	952	2
528.6.y	\(\chi_{528}(49, \cdot)\)	n/a	240	4
528.6.ba	\(\chi_{528}(79, \cdot)\)	n/a	240	4
528.6.bc	\(\chi_{528}(41, \cdot)\)	None	0	4
528.6.be	\(\chi_{528}(71, \cdot)\)	None	0	4
528.6.bh	\(\chi_{528}(7, \cdot)\)	None	0	4
528.6.bj	\(\chi_{528}(25, \cdot)\)	None	0	4
528.6.bl	\(\chi_{528}(47, \cdot)\)	n/a	480	4
528.6.bn	\(\chi_{528}(17, \cdot)\)	n/a	472	4
528.6.bo	\(\chi_{528}(29, \cdot)\)	n/a	3808	8
528.6.br	\(\chi_{528}(59, \cdot)\)	n/a	3808	8
528.6.bs	\(\chi_{528}(37, \cdot)\)	n/a	1920	8
528.6.bv	\(\chi_{528}(19, \cdot)\)	n/a	1920	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(528))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(528)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)