Space of modular forms of level 735 and weight 2

• Label: 735.2
• Level: 735
• Weight: 2
• Dimension: 12120
• Nonzero newspaces: 24
• Newform subspaces: 118
• Sturm bound: 75264
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 118 \)
Sturm bound:			\(75264\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(735))\).

	Total	New	Old
Modular forms	19776	12704	7072
Cusp forms	17857	12120	5737
Eisenstein series	1919	584	1335

Trace form

12120 * q - 4 * q^2 - 28 * q^3 - 36 * q^4 + 12 * q^5 - 56 * q^6 - 56 * q^7 + 60 * q^8 - 2 * q^9 - 34 * q^10 + 56 * q^11 + 16 * q^12 + 4 * q^13 + 48 * q^14 - 71 * q^15 - 68 * q^16 + 32 * q^17 - 22 * q^18 + 4 * q^19 + 64 * q^20 - 94 * q^21 + 4 * q^22 + 72 * q^23 - 60 * q^24 - 54 * q^25 + 32 * q^26 - 76 * q^27 - 24 * q^28 + 16 * q^29 - 137 * q^30 - 132 * q^31 - 92 * q^32 - 74 * q^33 - 92 * q^34 - 30 * q^35 - 346 * q^36 - 180 * q^37 - 208 * q^38 - 192 * q^39 - 462 * q^40 - 200 * q^41 - 246 * q^42 - 204 * q^43 - 440 * q^44 - 141 * q^45 - 540 * q^46 - 40 * q^47 - 454 * q^48 - 300 * q^49 - 52 * q^50 - 218 * q^51 - 572 * q^52 - 40 * q^53 - 20 * q^54 - 256 * q^55 - 396 * q^56 - 58 * q^57 - 508 * q^58 - 88 * q^59 - 315 * q^60 - 456 * q^61 - 168 * q^62 - 24 * q^63 - 508 * q^64 - 124 * q^65 - 262 * q^66 - 212 * q^67 - 128 * q^68 - 162 * q^69 - 354 * q^70 - 32 * q^71 - 150 * q^72 - 308 * q^73 - 224 * q^74 - 241 * q^75 - 316 * q^76 - 386 * q^78 - 188 * q^79 - 230 * q^80 - 278 * q^81 - 496 * q^82 - 264 * q^83 - 424 * q^84 - 274 * q^85 - 412 * q^86 - 262 * q^87 - 768 * q^88 - 192 * q^89 - 226 * q^90 - 332 * q^91 - 84 * q^92 - 354 * q^93 - 320 * q^94 - 124 * q^95 - 166 * q^96 - 136 * q^97 - 876 * q^98 - 184 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)

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
735.2.a	\(\chi_{735}(1, \cdot)\)	735.2.a.a	1	1
		735.2.a.b	1
		735.2.a.c	1
		735.2.a.d	1
		735.2.a.e	1
		735.2.a.f	1
		735.2.a.g	2
		735.2.a.h	2
		735.2.a.i	2
		735.2.a.j	2
		735.2.a.k	2
		735.2.a.l	2
		735.2.a.m	2
		735.2.a.n	4
		735.2.a.o	4
735.2.b	\(\chi_{735}(146, \cdot)\)	735.2.b.a	2	1
		735.2.b.b	2
		735.2.b.c	8
		735.2.b.d	8
		735.2.b.e	16
		735.2.b.f	16
735.2.d	\(\chi_{735}(589, \cdot)\)	735.2.d.a	2	1
		735.2.d.b	6
		735.2.d.c	8
		735.2.d.d	8
		735.2.d.e	8
		735.2.d.f	8
735.2.g	\(\chi_{735}(734, \cdot)\)	735.2.g.a	16	1
		735.2.g.b	24
		735.2.g.c	32
735.2.i	\(\chi_{735}(226, \cdot)\)	735.2.i.a	2	2
		735.2.i.b	2
		735.2.i.c	2
		735.2.i.d	2
		735.2.i.e	2
		735.2.i.f	2
		735.2.i.g	4
		735.2.i.h	4
		735.2.i.i	4
		735.2.i.j	4
		735.2.i.k	4
		735.2.i.l	4
		735.2.i.m	8
		735.2.i.n	8
735.2.j	\(\chi_{735}(197, \cdot)\)	735.2.j.a	8	2
		735.2.j.b	8
		735.2.j.c	16
		735.2.j.d	16
		735.2.j.e	24
		735.2.j.f	24
		735.2.j.g	24
		735.2.j.h	24
735.2.m	\(\chi_{735}(97, \cdot)\)	735.2.m.a	24	2
		735.2.m.b	24
		735.2.m.c	32
735.2.p	\(\chi_{735}(374, \cdot)\)	735.2.p.a	8	2
		735.2.p.b	8
		735.2.p.c	8
		735.2.p.d	16
		735.2.p.e	16
		735.2.p.f	24
		735.2.p.g	64
735.2.q	\(\chi_{735}(79, \cdot)\)	735.2.q.a	4	2
		735.2.q.b	4
		735.2.q.c	8
		735.2.q.d	8
		735.2.q.e	12
		735.2.q.f	12
		735.2.q.g	16
		735.2.q.h	16
735.2.s	\(\chi_{735}(521, \cdot)\)	735.2.s.a	2	2
		735.2.s.b	2
		735.2.s.c	2
		735.2.s.d	2
		735.2.s.e	2
		735.2.s.f	2
		735.2.s.g	4
		735.2.s.h	4
		735.2.s.i	4
		735.2.s.j	4
		735.2.s.k	8
		735.2.s.l	8
		735.2.s.m	32
		735.2.s.n	32
735.2.u	\(\chi_{735}(106, \cdot)\)	735.2.u.a	48	6
		735.2.u.b	48
		735.2.u.c	60
		735.2.u.d	60
735.2.v	\(\chi_{735}(178, \cdot)\)	735.2.v.a	32	4
		735.2.v.b	32
		735.2.v.c	48
		735.2.v.d	48
735.2.y	\(\chi_{735}(128, \cdot)\)	735.2.y.a	8	4
		735.2.y.b	8
		735.2.y.c	8
		735.2.y.d	8
		735.2.y.e	32
		735.2.y.f	32
		735.2.y.g	48
		735.2.y.h	48
		735.2.y.i	48
		735.2.y.j	48
735.2.ba	\(\chi_{735}(104, \cdot)\)	735.2.ba.a	648	6
735.2.bd	\(\chi_{735}(64, \cdot)\)	735.2.bd.a	336	6
735.2.bf	\(\chi_{735}(41, \cdot)\)	735.2.bf.a	228	6
		735.2.bf.b	228
735.2.bg	\(\chi_{735}(16, \cdot)\)	735.2.bg.a	108	12
		735.2.bg.b	108
		735.2.bg.c	120
		735.2.bg.d	120
735.2.bi	\(\chi_{735}(13, \cdot)\)	735.2.bi.a	672	12
735.2.bj	\(\chi_{735}(8, \cdot)\)	735.2.bj.a	1296	12
735.2.bm	\(\chi_{735}(26, \cdot)\)	735.2.bm.a	444	12
		735.2.bm.b	444
735.2.bo	\(\chi_{735}(4, \cdot)\)	735.2.bo.a	672	12
735.2.bp	\(\chi_{735}(59, \cdot)\)	735.2.bp.a	1296	12
735.2.bt	\(\chi_{735}(2, \cdot)\)	735.2.bt.a	2592	24
735.2.bu	\(\chi_{735}(52, \cdot)\)	735.2.bu.a	1344	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(735))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(735)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 1}\)