Space of modular forms of level 528 and weight 4

• Label: 528.4
• Level: 528
• Weight: 4
• Dimension: 9476
• Nonzero newspaces: 16
• Sturm bound: 61440
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(61440\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(528))\).

	Total	New	Old
Modular forms	23600	9640	13960
Cusp forms	22480	9476	13004
Eisenstein series	1120	164	956

Trace form

9476 * q - 5 * q^3 + 8 * q^4 - 4 * q^5 - 76 * q^6 - 78 * q^7 - 168 * q^8 - 119 * q^9 - 296 * q^10 + 60 * q^11 + 168 * q^12 - 22 * q^13 + 696 * q^14 - 315 * q^15 + 568 * q^16 + 52 * q^17 - 52 * q^18 - 94 * q^19 - 160 * q^20 + 500 * q^21 - 704 * q^22 + 496 * q^23 - 236 * q^24 + 432 * q^25 + 40 * q^26 + 307 * q^27 + 1240 * q^28 - 116 * q^29 + 1460 * q^30 + 1410 * q^31 + 1920 * q^32 + 735 * q^33 + 288 * q^34 + 1500 * q^35 + 972 * q^36 - 2318 * q^37 - 2512 * q^38 - 3319 * q^39 - 4792 * q^40 - 3788 * q^41 - 2732 * q^42 - 3420 * q^43 + 200 * q^44 + 262 * q^45 + 1496 * q^46 - 708 * q^47 - 1364 * q^48 + 1716 * q^49 - 1416 * q^50 + 1929 * q^51 - 2696 * q^52 - 588 * q^53 - 3420 * q^54 + 4062 * q^55 - 2688 * q^56 - 1785 * q^57 - 3064 * q^58 + 1256 * q^59 + 828 * q^60 + 1322 * q^61 + 1992 * q^62 + 417 * q^63 + 4184 * q^64 - 696 * q^65 + 2016 * q^66 + 9284 * q^67 + 3136 * q^68 + 8502 * q^69 + 144 * q^70 - 1124 * q^71 + 2492 * q^72 - 10046 * q^73 - 13520 * q^74 - 5737 * q^75 - 9544 * q^76 - 6352 * q^77 + 5720 * q^78 - 10594 * q^79 + 12216 * q^80 - 775 * q^81 + 21304 * q^82 - 5036 * q^83 + 18572 * q^84 + 15526 * q^85 + 30624 * q^86 + 200 * q^87 + 50712 * q^88 + 13732 * q^89 - 180 * q^90 + 17290 * q^91 + 10848 * q^92 + 15159 * q^93 - 216 * q^94 + 24972 * q^95 - 18796 * q^96 + 514 * q^97 - 23640 * q^98 - 1571 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(528))\)

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
528.4.a	\(\chi_{528}(1, \cdot)\)	528.4.a.a	1	1
		528.4.a.b	1
		528.4.a.c	1
		528.4.a.d	1
		528.4.a.e	1
		528.4.a.f	1
		528.4.a.g	1
		528.4.a.h	1
		528.4.a.i	1
		528.4.a.j	1
		528.4.a.k	1
		528.4.a.l	1
		528.4.a.m	2
		528.4.a.n	2
		528.4.a.o	2
		528.4.a.p	2
		528.4.a.q	2
		528.4.a.r	2
		528.4.a.s	3
		528.4.a.t	3
528.4.b	\(\chi_{528}(65, \cdot)\)	528.4.b.a	2	1
		528.4.b.b	4
		528.4.b.c	6
		528.4.b.d	6
		528.4.b.e	8
		528.4.b.f	8
		528.4.b.g	18
		528.4.b.h	18
528.4.d	\(\chi_{528}(287, \cdot)\)	528.4.d.a	10	1
		528.4.d.b	10
		528.4.d.c	20
		528.4.d.d	20
528.4.f	\(\chi_{528}(265, \cdot)\)	None	0	1
528.4.h	\(\chi_{528}(439, \cdot)\)	None	0	1
528.4.k	\(\chi_{528}(23, \cdot)\)	None	0	1
528.4.m	\(\chi_{528}(329, \cdot)\)	None	0	1
528.4.o	\(\chi_{528}(175, \cdot)\)	528.4.o.a	12	1
		528.4.o.b	24
528.4.q	\(\chi_{528}(43, \cdot)\)	n/a	288	2
528.4.t	\(\chi_{528}(133, \cdot)\)	n/a	240	2
528.4.u	\(\chi_{528}(155, \cdot)\)	n/a	480	2
528.4.x	\(\chi_{528}(197, \cdot)\)	n/a	568	2
528.4.y	\(\chi_{528}(49, \cdot)\)	n/a	144	4
528.4.ba	\(\chi_{528}(79, \cdot)\)	n/a	144	4
528.4.bc	\(\chi_{528}(41, \cdot)\)	None	0	4
528.4.be	\(\chi_{528}(71, \cdot)\)	None	0	4
528.4.bh	\(\chi_{528}(7, \cdot)\)	None	0	4
528.4.bj	\(\chi_{528}(25, \cdot)\)	None	0	4
528.4.bl	\(\chi_{528}(47, \cdot)\)	n/a	288	4
528.4.bn	\(\chi_{528}(17, \cdot)\)	n/a	280	4
528.4.bo	\(\chi_{528}(29, \cdot)\)	n/a	2272	8
528.4.br	\(\chi_{528}(59, \cdot)\)	n/a	2272	8
528.4.bs	\(\chi_{528}(37, \cdot)\)	n/a	1152	8
528.4.bv	\(\chi_{528}(19, \cdot)\)	n/a	1152	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(528))\) into lower level spaces

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