Space of modular forms of level 567 and weight 2

• Label: 567.2
• Level: 567
• Weight: 2
• Dimension: 8552
• Nonzero newspaces: 22
• Newform subspaces: 98
• Sturm bound: 46656
• Trace bound: 21

Defining parameters

Level:	\( N \)	=	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 22 \)
Newform subspaces:			\( 98 \)
Sturm bound:			\(46656\)
Trace bound:			\(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(567))\).

	Total	New	Old
Modular forms	12312	9112	3200
Cusp forms	11017	8552	2465
Eisenstein series	1295	560	735

Trace form

8552 * q - 48 * q^2 - 72 * q^3 - 76 * q^4 - 42 * q^5 - 72 * q^6 - 97 * q^7 - 96 * q^8 - 72 * q^9 - 96 * q^10 - 30 * q^11 - 72 * q^12 - 62 * q^13 - 39 * q^14 - 180 * q^15 - 76 * q^16 - 18 * q^17 - 90 * q^18 - 128 * q^19 - 114 * q^20 - 117 * q^21 - 210 * q^22 - 114 * q^23 - 180 * q^24 - 100 * q^25 - 222 * q^26 - 126 * q^27 - 169 * q^28 - 174 * q^29 - 180 * q^30 - 98 * q^31 - 144 * q^32 - 126 * q^33 - 102 * q^34 - 69 * q^35 - 252 * q^36 - 92 * q^37 + 30 * q^38 - 72 * q^39 - 150 * q^40 - 42 * q^41 - 135 * q^42 - 194 * q^43 - 174 * q^44 - 180 * q^45 - 204 * q^46 - 174 * q^47 - 270 * q^48 - 145 * q^49 - 480 * q^50 - 198 * q^51 - 230 * q^52 - 288 * q^53 - 324 * q^54 - 276 * q^55 - 411 * q^56 - 288 * q^57 - 234 * q^58 - 276 * q^59 - 306 * q^60 - 164 * q^61 - 420 * q^62 - 144 * q^63 - 460 * q^64 - 192 * q^65 - 72 * q^66 - 152 * q^67 - 72 * q^68 + 36 * q^69 - 249 * q^70 + 18 * q^71 + 360 * q^72 - 110 * q^73 + 210 * q^74 + 108 * q^75 - 194 * q^76 + 51 * q^77 + 54 * q^78 - 92 * q^79 + 444 * q^80 + 72 * q^81 - 120 * q^82 + 186 * q^83 + 135 * q^84 - 258 * q^85 + 354 * q^86 + 216 * q^87 - 234 * q^88 + 108 * q^89 + 90 * q^90 - 140 * q^91 + 66 * q^92 - 108 * q^93 - 162 * q^94 - 174 * q^95 - 54 * q^96 - 182 * q^97 - 219 * q^98 - 324 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(567))\)

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
567.2.a	\(\chi_{567}(1, \cdot)\)	567.2.a.a	1	1
		567.2.a.b	1
		567.2.a.c	3
		567.2.a.d	3
		567.2.a.e	3
		567.2.a.f	3
		567.2.a.g	3
		567.2.a.h	3
		567.2.a.i	4
567.2.c	\(\chi_{567}(566, \cdot)\)	567.2.c.a	8	1
		567.2.c.b	8
		567.2.c.c	12
567.2.e	\(\chi_{567}(163, \cdot)\)	567.2.e.a	2	2
		567.2.e.b	2
		567.2.e.c	8
		567.2.e.d	8
		567.2.e.e	10
		567.2.e.f	10
		567.2.e.g	16
567.2.f	\(\chi_{567}(190, \cdot)\)	567.2.f.a	2	2
		567.2.f.b	2
		567.2.f.c	2
		567.2.f.d	2
		567.2.f.e	2
		567.2.f.f	2
		567.2.f.g	2
		567.2.f.h	2
		567.2.f.i	4
		567.2.f.j	4
		567.2.f.k	4
		567.2.f.l	6
		567.2.f.m	6
		567.2.f.n	8
567.2.g	\(\chi_{567}(109, \cdot)\)	567.2.g.a	2	2
		567.2.g.b	2
		567.2.g.c	2
		567.2.g.d	2
		567.2.g.e	2
		567.2.g.f	2
		567.2.g.g	4
		567.2.g.h	6
		567.2.g.i	6
		567.2.g.j	8
		567.2.g.k	8
		567.2.g.l	16
567.2.h	\(\chi_{567}(298, \cdot)\)	567.2.h.a	2	2
		567.2.h.b	2
		567.2.h.c	2
		567.2.h.d	2
		567.2.h.e	2
		567.2.h.f	2
		567.2.h.g	4
		567.2.h.h	6
		567.2.h.i	6
		567.2.h.j	8
		567.2.h.k	8
		567.2.h.l	16
567.2.i	\(\chi_{567}(215, \cdot)\)	567.2.i.a	2	2
		567.2.i.b	2
		567.2.i.c	4
		567.2.i.d	4
		567.2.i.e	4
		567.2.i.f	12
		567.2.i.g	32
567.2.o	\(\chi_{567}(188, \cdot)\)	567.2.o.a	2	2
		567.2.o.b	2
		567.2.o.c	4
		567.2.o.d	4
		567.2.o.e	8
		567.2.o.f	8
		567.2.o.g	16
		567.2.o.h	16
567.2.p	\(\chi_{567}(80, \cdot)\)	567.2.p.a	2	2
		567.2.p.b	2
		567.2.p.c	10
		567.2.p.d	10
		567.2.p.e	32
567.2.s	\(\chi_{567}(26, \cdot)\)	567.2.s.a	2	2
		567.2.s.b	2
		567.2.s.c	4
		567.2.s.d	4
		567.2.s.e	4
		567.2.s.f	12
		567.2.s.g	32
567.2.u	\(\chi_{567}(100, \cdot)\)	567.2.u.a	132	6
567.2.v	\(\chi_{567}(64, \cdot)\)	567.2.v.a	54	6
		567.2.v.b	54
567.2.w	\(\chi_{567}(37, \cdot)\)	567.2.w.a	132	6
567.2.ba	\(\chi_{567}(143, \cdot)\)	567.2.ba.a	132	6
567.2.bd	\(\chi_{567}(17, \cdot)\)	567.2.bd.a	132	6
567.2.be	\(\chi_{567}(62, \cdot)\)	567.2.be.a	132	6
567.2.bg	\(\chi_{567}(4, \cdot)\)	567.2.bg.a	1260	18
567.2.bh	\(\chi_{567}(22, \cdot)\)	567.2.bh.a	486	18
		567.2.bh.b	486
567.2.bi	\(\chi_{567}(25, \cdot)\)	567.2.bi.a	1260	18
567.2.bl	\(\chi_{567}(47, \cdot)\)	567.2.bl.a	1260	18
567.2.bm	\(\chi_{567}(20, \cdot)\)	567.2.bm.a	1260	18
567.2.br	\(\chi_{567}(5, \cdot)\)	567.2.br.a	1260	18

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(567))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(567)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)