Space of modular forms of level 532 and weight 2

• Label: 532.2
• Level: 532
• Weight: 2
• Dimension: 4634
• Nonzero newspaces: 32
• Newform subspaces: 57
• Sturm bound: 34560
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Newform subspaces:			\( 57 \)
Sturm bound:			\(34560\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(532))\).

	Total	New	Old
Modular forms	9180	4970	4210
Cusp forms	8101	4634	3467
Eisenstein series	1079	336	743

Trace form

4634 * q - 30 * q^2 + 2 * q^3 - 30 * q^4 - 54 * q^5 - 36 * q^6 + 8 * q^7 - 84 * q^8 - 64 * q^9 - 48 * q^10 - 6 * q^11 - 60 * q^12 - 56 * q^13 - 63 * q^14 + 24 * q^15 - 54 * q^16 - 36 * q^17 - 60 * q^18 + 41 * q^19 - 72 * q^20 - 79 * q^21 - 54 * q^22 + 24 * q^23 - 12 * q^24 - 40 * q^25 - 12 * q^26 + 26 * q^27 - 18 * q^28 - 216 * q^29 - 150 * q^30 - 50 * q^31 - 120 * q^32 - 198 * q^33 - 126 * q^34 - 66 * q^35 - 288 * q^36 - 158 * q^37 - 180 * q^38 - 104 * q^39 - 186 * q^40 - 132 * q^41 - 159 * q^42 - 50 * q^43 - 162 * q^44 - 138 * q^45 - 150 * q^46 - 162 * q^48 - 76 * q^49 - 150 * q^50 + 78 * q^51 - 36 * q^52 + 42 * q^53 + 54 * q^54 + 108 * q^55 - 72 * q^56 - 52 * q^57 - 60 * q^58 + 108 * q^59 - 30 * q^60 - 50 * q^61 + 54 * q^62 + 32 * q^63 + 36 * q^64 - 102 * q^65 + 120 * q^66 - 44 * q^67 + 90 * q^68 - 318 * q^69 + 51 * q^70 + 18 * q^71 + 264 * q^72 - 290 * q^73 + 96 * q^74 - 76 * q^75 + 144 * q^76 - 339 * q^77 + 6 * q^78 - 74 * q^79 + 156 * q^80 - 232 * q^81 + 210 * q^82 - 30 * q^83 + 63 * q^84 - 456 * q^85 + 126 * q^86 + 60 * q^87 + 72 * q^88 - 204 * q^89 + 18 * q^90 + 28 * q^91 + 12 * q^92 - 38 * q^93 + 6 * q^94 - 21 * q^95 - 168 * q^96 - 50 * q^97 - 114 * q^98 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)

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
532.2.a	\(\chi_{532}(1, \cdot)\)	532.2.a.a	1	1
		532.2.a.b	2
		532.2.a.c	2
		532.2.a.d	2
		532.2.a.e	3
532.2.f	\(\chi_{532}(419, \cdot)\)	532.2.f.a	4	1
		532.2.f.b	4
		532.2.f.c	32
		532.2.f.d	32
532.2.g	\(\chi_{532}(265, \cdot)\)	532.2.g.a	4	1
		532.2.g.b	8
532.2.h	\(\chi_{532}(379, \cdot)\)	532.2.h.a	4	1
		532.2.h.b	4
		532.2.h.c	52
532.2.i	\(\chi_{532}(305, \cdot)\)	532.2.i.a	4	2
		532.2.i.b	6
		532.2.i.c	14
532.2.j	\(\chi_{532}(197, \cdot)\)	532.2.j.a	2	2
		532.2.j.b	8
		532.2.j.c	10
532.2.k	\(\chi_{532}(121, \cdot)\)	532.2.k.a	4	2
		532.2.k.b	24
532.2.l	\(\chi_{532}(429, \cdot)\)	532.2.l.a	4	2
		532.2.l.b	24
532.2.q	\(\chi_{532}(145, \cdot)\)	532.2.q.a	28	2
532.2.r	\(\chi_{532}(87, \cdot)\)	532.2.r.a	4	2
		532.2.r.b	148
532.2.s	\(\chi_{532}(183, \cdot)\)	532.2.s.a	120	2
532.2.t	\(\chi_{532}(151, \cdot)\)	532.2.t.a	152	2
532.2.u	\(\chi_{532}(83, \cdot)\)	532.2.u.a	16	2
		532.2.u.b	136
532.2.v	\(\chi_{532}(341, \cdot)\)	532.2.v.a	2	2
		532.2.v.b	2
		532.2.v.c	4
		532.2.v.d	4
		532.2.v.e	16
532.2.w	\(\chi_{532}(115, \cdot)\)	532.2.w.a	72	2
		532.2.w.b	72
532.2.x	\(\chi_{532}(69, \cdot)\)	532.2.x.a	24	2
532.2.y	\(\chi_{532}(107, \cdot)\)	532.2.y.a	152	2
532.2.bl	\(\chi_{532}(331, \cdot)\)	532.2.bl.a	152	2
532.2.bm	\(\chi_{532}(297, \cdot)\)	532.2.bm.a	28	2
532.2.bn	\(\chi_{532}(311, \cdot)\)	532.2.bn.a	4	2
		532.2.bn.b	148
532.2.bo	\(\chi_{532}(85, \cdot)\)	532.2.bo.a	30	6
		532.2.bo.b	30
532.2.bp	\(\chi_{532}(9, \cdot)\)	532.2.bp.a	78	6
532.2.bq	\(\chi_{532}(25, \cdot)\)	532.2.bq.a	78	6
532.2.br	\(\chi_{532}(131, \cdot)\)	532.2.br.a	456	6
532.2.bs	\(\chi_{532}(67, \cdot)\)	532.2.bs.a	456	6
532.2.bv	\(\chi_{532}(13, \cdot)\)	532.2.bv.a	84	6
532.2.bw	\(\chi_{532}(89, \cdot)\)	532.2.bw.a	78	6
532.2.cb	\(\chi_{532}(15, \cdot)\)	532.2.cb.a	360	6
532.2.cc	\(\chi_{532}(55, \cdot)\)	532.2.cc.a	456	6
532.2.cd	\(\chi_{532}(47, \cdot)\)	532.2.cd.a	456	6
532.2.ce	\(\chi_{532}(51, \cdot)\)	532.2.ce.a	456	6
532.2.cj	\(\chi_{532}(33, \cdot)\)	532.2.cj.a	78	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(532))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(532)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)