Space of modular forms of level 765 and weight 2

• Label: 765.2
• Level: 765
• Weight: 2
• Dimension: 14538
• Nonzero newspaces: 36
• Newform subspaces: 102
• Sturm bound: 82944
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Newform subspaces:			\( 102 \)
Sturm bound:			\(82944\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(765))\).

	Total	New	Old
Modular forms	21760	15350	6410
Cusp forms	19713	14538	5175
Eisenstein series	2047	812	1235

Trace form

14538 * q - 34 * q^2 - 48 * q^3 - 26 * q^4 - 54 * q^5 - 160 * q^6 - 24 * q^7 - 42 * q^8 - 56 * q^9 - 182 * q^10 - 120 * q^11 - 80 * q^12 - 28 * q^13 - 40 * q^14 - 104 * q^15 - 58 * q^16 - 34 * q^17 - 160 * q^18 - 88 * q^19 - 94 * q^20 - 192 * q^21 - 32 * q^22 - 56 * q^23 - 136 * q^24 - 50 * q^25 - 100 * q^26 - 96 * q^27 - 64 * q^28 - 52 * q^29 - 160 * q^30 - 64 * q^31 - 90 * q^32 - 80 * q^33 + 66 * q^34 - 96 * q^35 - 128 * q^36 - 84 * q^37 + 16 * q^38 - 64 * q^39 - 58 * q^40 - 148 * q^41 - 184 * q^42 - 32 * q^43 - 232 * q^44 - 104 * q^45 - 512 * q^46 - 208 * q^47 - 304 * q^48 - 246 * q^49 - 82 * q^50 - 304 * q^51 - 484 * q^52 - 220 * q^53 - 280 * q^54 - 304 * q^55 - 592 * q^56 - 256 * q^57 - 180 * q^58 - 264 * q^59 - 264 * q^60 - 196 * q^61 - 392 * q^62 - 280 * q^63 - 402 * q^64 - 184 * q^65 - 464 * q^66 - 16 * q^67 + 34 * q^68 - 248 * q^69 - 184 * q^70 - 240 * q^71 - 240 * q^72 - 100 * q^73 - 20 * q^74 - 80 * q^75 - 232 * q^76 + 8 * q^77 + 16 * q^78 - 24 * q^79 - 306 * q^80 - 112 * q^81 - 140 * q^82 + 64 * q^83 - 80 * q^84 - 294 * q^85 - 632 * q^86 - 168 * q^87 - 624 * q^88 - 252 * q^89 - 128 * q^90 - 816 * q^91 - 688 * q^92 - 200 * q^93 - 744 * q^94 - 328 * q^95 - 688 * q^96 - 308 * q^97 - 770 * q^98 - 312 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(765))\)

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
765.2.a	\(\chi_{765}(1, \cdot)\)	765.2.a.a	1	1
		765.2.a.b	1
		765.2.a.c	1
		765.2.a.d	2
		765.2.a.e	2
		765.2.a.f	2
		765.2.a.g	2
		765.2.a.h	2
		765.2.a.i	2
		765.2.a.j	3
		765.2.a.k	3
		765.2.a.l	3
		765.2.a.m	4
765.2.b	\(\chi_{765}(154, \cdot)\)	765.2.b.a	2	1
		765.2.b.b	4
		765.2.b.c	8
		765.2.b.d	10
		765.2.b.e	16
765.2.d	\(\chi_{765}(424, \cdot)\)	765.2.d.a	4	1
		765.2.d.b	4
		765.2.d.c	8
		765.2.d.d	8
		765.2.d.e	8
		765.2.d.f	12
765.2.g	\(\chi_{765}(271, \cdot)\)	765.2.g.a	4	1
		765.2.g.b	6
		765.2.g.c	8
		765.2.g.d	12
765.2.i	\(\chi_{765}(256, \cdot)\)	765.2.i.a	2	2
		765.2.i.b	2
		765.2.i.c	26
		765.2.i.d	26
		765.2.i.e	34
		765.2.i.f	38
765.2.k	\(\chi_{765}(361, \cdot)\)	765.2.k.a	8	2
		765.2.k.b	12
		765.2.k.c	16
		765.2.k.d	24
765.2.l	\(\chi_{765}(98, \cdot)\)	765.2.l.a	4	2
		765.2.l.b	68
765.2.n	\(\chi_{765}(188, \cdot)\)	765.2.n.a	8	2
		765.2.n.b	8
		765.2.n.c	8
		765.2.n.d	16
		765.2.n.e	24
765.2.p	\(\chi_{765}(152, \cdot)\)	765.2.p.a	72	2
765.2.s	\(\chi_{765}(548, \cdot)\)	765.2.s.a	4	2
		765.2.s.b	68
765.2.t	\(\chi_{765}(64, \cdot)\)	765.2.t.a	2	2
		765.2.t.b	2
		765.2.t.c	8
		765.2.t.d	8
		765.2.t.e	12
		765.2.t.f	24
		765.2.t.g	32
765.2.w	\(\chi_{765}(16, \cdot)\)	765.2.w.a	4	2
		765.2.w.b	8
		765.2.w.c	132
765.2.z	\(\chi_{765}(169, \cdot)\)	765.2.z.a	208	2
765.2.bb	\(\chi_{765}(409, \cdot)\)	765.2.bb.a	4	2
		765.2.bb.b	188
765.2.bd	\(\chi_{765}(53, \cdot)\)	765.2.bd.a	72	4
		765.2.bd.b	72
765.2.be	\(\chi_{765}(406, \cdot)\)	765.2.be.a	16	4
		765.2.be.b	24
		765.2.be.c	32
		765.2.be.d	48
765.2.bh	\(\chi_{765}(19, \cdot)\)	765.2.bh.a	16	4
		765.2.bh.b	24
		765.2.bh.c	48
		765.2.bh.d	80
765.2.bi	\(\chi_{765}(8, \cdot)\)	765.2.bi.a	72	4
		765.2.bi.b	72
765.2.bl	\(\chi_{765}(4, \cdot)\)	765.2.bl.a	416	4
765.2.bm	\(\chi_{765}(38, \cdot)\)	765.2.bm.a	4	4
		765.2.bm.b	4
		765.2.bm.c	408
765.2.bo	\(\chi_{765}(203, \cdot)\)	765.2.bo.a	416	4
765.2.bq	\(\chi_{765}(137, \cdot)\)	765.2.bq.a	384	4
765.2.bt	\(\chi_{765}(353, \cdot)\)	765.2.bt.a	4	4
		765.2.bt.b	4
		765.2.bt.c	408
765.2.bu	\(\chi_{765}(106, \cdot)\)	765.2.bu.a	8	4
		765.2.bu.b	280
765.2.bx	\(\chi_{765}(73, \cdot)\)	765.2.bx.a	56	8
		765.2.bx.b	144
		765.2.bx.c	144
765.2.by	\(\chi_{765}(44, \cdot)\)	765.2.by.a	144	8
		765.2.by.b	144
765.2.ca	\(\chi_{765}(71, \cdot)\)	765.2.ca.a	96	8
		765.2.ca.b	96
765.2.cc	\(\chi_{765}(28, \cdot)\)	765.2.cc.a	56	8
		765.2.cc.b	144
		765.2.cc.c	144
765.2.cf	\(\chi_{765}(2, \cdot)\)	765.2.cf.a	832	8
765.2.cg	\(\chi_{765}(49, \cdot)\)	765.2.cg.a	832	8
765.2.cj	\(\chi_{765}(76, \cdot)\)	765.2.cj.a	576	8
765.2.ck	\(\chi_{765}(77, \cdot)\)	765.2.ck.a	832	8
765.2.cn	\(\chi_{765}(22, \cdot)\)	765.2.cn.a	1664	16
765.2.cp	\(\chi_{765}(11, \cdot)\)	765.2.cp.a	1152	16
765.2.cr	\(\chi_{765}(14, \cdot)\)	765.2.cr.a	1664	16
765.2.cs	\(\chi_{765}(7, \cdot)\)	765.2.cs.a	1664	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(765))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(765)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)