Space of modular forms of level 528 and weight 2

• Label: 528.2
• Level: 528
• Weight: 2
• Dimension: 3104
• Nonzero newspaces: 16
• Newform subspaces: 57
• Sturm bound: 30720
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 57 \)
Sturm bound:			\(30720\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(528))\).

	Total	New	Old
Modular forms	8240	3268	4972
Cusp forms	7121	3104	4017
Eisenstein series	1119	164	955

Trace form

3104 * q - 13 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^6 - 14 * q^7 + 24 * q^8 + 5 * q^9 - 24 * q^10 + 12 * q^11 - 40 * q^12 - 30 * q^13 - 24 * q^14 + 5 * q^15 - 72 * q^16 - 4 * q^17 - 36 * q^18 + 2 * q^19 - 32 * q^20 - 28 * q^21 - 56 * q^22 - 16 * q^23 - 76 * q^24 - 28 * q^25 - 40 * q^26 - 37 * q^27 - 40 * q^28 + 20 * q^29 - 60 * q^30 - 62 * q^31 - 17 * q^33 - 64 * q^34 + 12 * q^35 - 52 * q^36 + 58 * q^37 + 16 * q^38 + 9 * q^39 + 8 * q^40 + 92 * q^41 + 68 * q^42 + 20 * q^43 + 40 * q^44 + 38 * q^45 + 56 * q^46 + 60 * q^47 + 108 * q^48 + 80 * q^49 + 72 * q^50 - 23 * q^51 + 24 * q^52 + 12 * q^53 + 76 * q^54 - 2 * q^55 + 31 * q^57 - 72 * q^58 - 56 * q^59 - 36 * q^60 - 158 * q^61 + 24 * q^62 - 31 * q^63 - 168 * q^64 + 24 * q^65 - 72 * q^66 - 92 * q^67 - 64 * q^68 - 66 * q^69 - 464 * q^70 - 4 * q^71 - 132 * q^72 - 230 * q^73 - 304 * q^74 - 17 * q^75 - 488 * q^76 - 176 * q^77 - 376 * q^78 - 98 * q^79 - 456 * q^80 - 59 * q^81 - 488 * q^82 - 28 * q^83 - 244 * q^84 - 394 * q^85 - 288 * q^86 + 8 * q^87 - 648 * q^88 - 148 * q^89 - 52 * q^90 - 22 * q^91 - 288 * q^92 - 153 * q^93 - 440 * q^94 + 12 * q^95 - 108 * q^96 - 262 * q^97 - 360 * q^98 + 29 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)

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
528.2.a	\(\chi_{528}(1, \cdot)\)	528.2.a.a	1	1
		528.2.a.b	1
		528.2.a.c	1
		528.2.a.d	1
		528.2.a.e	1
		528.2.a.f	1
		528.2.a.g	1
		528.2.a.h	1
		528.2.a.i	1
		528.2.a.j	1
528.2.b	\(\chi_{528}(65, \cdot)\)	528.2.b.a	2	1
		528.2.b.b	2
		528.2.b.c	2
		528.2.b.d	4
		528.2.b.e	6
		528.2.b.f	6
528.2.d	\(\chi_{528}(287, \cdot)\)	528.2.d.a	2	1
		528.2.d.b	2
		528.2.d.c	2
		528.2.d.d	2
		528.2.d.e	2
		528.2.d.f	2
		528.2.d.g	4
		528.2.d.h	4
528.2.f	\(\chi_{528}(265, \cdot)\)	None	0	1
528.2.h	\(\chi_{528}(439, \cdot)\)	None	0	1
528.2.k	\(\chi_{528}(23, \cdot)\)	None	0	1
528.2.m	\(\chi_{528}(329, \cdot)\)	None	0	1
528.2.o	\(\chi_{528}(175, \cdot)\)	528.2.o.a	4	1
		528.2.o.b	8
528.2.q	\(\chi_{528}(43, \cdot)\)	528.2.q.a	96	2
528.2.t	\(\chi_{528}(133, \cdot)\)	528.2.t.a	40	2
		528.2.t.b	40
528.2.u	\(\chi_{528}(155, \cdot)\)	528.2.u.a	160	2
528.2.x	\(\chi_{528}(197, \cdot)\)	528.2.x.a	184	2
528.2.y	\(\chi_{528}(49, \cdot)\)	528.2.y.a	4	4
		528.2.y.b	4
		528.2.y.c	4
		528.2.y.d	4
		528.2.y.e	4
		528.2.y.f	4
		528.2.y.g	4
		528.2.y.h	4
		528.2.y.i	4
		528.2.y.j	4
		528.2.y.k	8
528.2.ba	\(\chi_{528}(79, \cdot)\)	528.2.ba.a	8	4
		528.2.ba.b	8
		528.2.ba.c	32
528.2.bc	\(\chi_{528}(41, \cdot)\)	None	0	4
528.2.be	\(\chi_{528}(71, \cdot)\)	None	0	4
528.2.bh	\(\chi_{528}(7, \cdot)\)	None	0	4
528.2.bj	\(\chi_{528}(25, \cdot)\)	None	0	4
528.2.bl	\(\chi_{528}(47, \cdot)\)	528.2.bl.a	32	4
		528.2.bl.b	64
528.2.bn	\(\chi_{528}(17, \cdot)\)	528.2.bn.a	8	4
		528.2.bn.b	8
		528.2.bn.c	8
		528.2.bn.d	16
		528.2.bn.e	24
		528.2.bn.f	24
528.2.bo	\(\chi_{528}(29, \cdot)\)	528.2.bo.a	736	8
528.2.br	\(\chi_{528}(59, \cdot)\)	528.2.br.a	736	8
528.2.bs	\(\chi_{528}(37, \cdot)\)	528.2.bs.a	384	8
528.2.bv	\(\chi_{528}(19, \cdot)\)	528.2.bv.a	384	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(528))\) into lower level spaces

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