Space of modular forms of level 765 and weight 4

• Label: 765.4
• Level: 765
• Weight: 4
• Dimension: 44426
• Nonzero newspaces: 36
• Sturm bound: 165888
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(165888\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(765))\).

	Total	New	Old
Modular forms	63232	45238	17994
Cusp forms	61184	44426	16758
Eisenstein series	2048	812	1236

Trace form

44426 * q - 44 * q^2 - 60 * q^3 - 108 * q^4 - 84 * q^5 - 124 * q^6 + 96 * q^8 + 4 * q^9 - 288 * q^10 - 168 * q^11 - 416 * q^12 + 120 * q^13 + 328 * q^14 + 310 * q^15 + 172 * q^16 + 262 * q^17 + 752 * q^18 - 1056 * q^19 - 2120 * q^20 - 1212 * q^21 - 2276 * q^22 - 1360 * q^23 - 1012 * q^24 + 1932 * q^25 + 1696 * q^26 - 672 * q^27 + 3520 * q^28 + 2512 * q^29 + 2816 * q^30 + 1148 * q^31 + 2340 * q^32 + 2968 * q^33 - 4710 * q^34 - 48 * q^35 + 796 * q^36 - 4252 * q^37 - 8164 * q^38 - 5332 * q^39 - 9808 * q^40 - 9860 * q^41 - 13024 * q^42 + 148 * q^43 + 40 * q^44 - 4670 * q^45 + 6688 * q^46 + 784 * q^47 + 4460 * q^48 + 7942 * q^49 - 1736 * q^50 + 6338 * q^51 + 24176 * q^52 + 16108 * q^53 + 20756 * q^54 + 10196 * q^55 + 27112 * q^56 + 6812 * q^57 + 9832 * q^58 + 1848 * q^59 + 912 * q^60 - 7896 * q^61 - 23032 * q^62 - 5620 * q^63 - 36744 * q^64 - 7826 * q^65 - 8360 * q^66 - 10500 * q^67 - 16030 * q^68 + 3436 * q^69 - 21588 * q^70 + 3912 * q^71 + 9516 * q^72 - 15644 * q^73 - 2080 * q^74 + 8254 * q^75 + 8868 * q^76 + 11740 * q^77 + 8104 * q^78 + 14900 * q^79 + 23976 * q^80 - 2044 * q^81 + 42104 * q^82 - 3952 * q^83 - 51992 * q^84 + 728 * q^85 - 88180 * q^86 - 43212 * q^87 - 38172 * q^88 - 45972 * q^89 - 50840 * q^90 - 23280 * q^91 - 21896 * q^92 - 12188 * q^93 + 22872 * q^94 + 7936 * q^95 + 33920 * q^96 + 10172 * q^97 + 63392 * q^98 + 27564 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(765))\)

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
765.4.a	\(\chi_{765}(1, \cdot)\)	765.4.a.a	1	1
		765.4.a.b	1
		765.4.a.c	1
		765.4.a.d	1
		765.4.a.e	1
		765.4.a.f	2
		765.4.a.g	2
		765.4.a.h	2
		765.4.a.i	2
		765.4.a.j	2
		765.4.a.k	3
		765.4.a.l	3
		765.4.a.m	5
		765.4.a.n	5
		765.4.a.o	5
		765.4.a.p	6
		765.4.a.q	6
		765.4.a.r	7
		765.4.a.s	7
		765.4.a.t	9
		765.4.a.u	9
765.4.b	\(\chi_{765}(154, \cdot)\)	n/a	120	1
765.4.d	\(\chi_{765}(424, \cdot)\)	n/a	132	1
765.4.g	\(\chi_{765}(271, \cdot)\)	765.4.g.a	2	1
		765.4.g.b	16
		765.4.g.c	16
		765.4.g.d	20
		765.4.g.e	36
765.4.i	\(\chi_{765}(256, \cdot)\)	n/a	384	2
765.4.k	\(\chi_{765}(361, \cdot)\)	n/a	180	2
765.4.l	\(\chi_{765}(98, \cdot)\)	n/a	216	2
765.4.n	\(\chi_{765}(188, \cdot)\)	n/a	192	2
765.4.p	\(\chi_{765}(152, \cdot)\)	n/a	216	2
765.4.s	\(\chi_{765}(548, \cdot)\)	n/a	216	2
765.4.t	\(\chi_{765}(64, \cdot)\)	n/a	264	2
765.4.w	\(\chi_{765}(16, \cdot)\)	n/a	432	2
765.4.z	\(\chi_{765}(169, \cdot)\)	n/a	640	2
765.4.bb	\(\chi_{765}(409, \cdot)\)	n/a	576	2
765.4.bd	\(\chi_{765}(53, \cdot)\)	n/a	432	4
765.4.be	\(\chi_{765}(406, \cdot)\)	n/a	360	4
765.4.bh	\(\chi_{765}(19, \cdot)\)	n/a	536	4
765.4.bi	\(\chi_{765}(8, \cdot)\)	n/a	432	4
765.4.bl	\(\chi_{765}(4, \cdot)\)	n/a	1280	4
765.4.bm	\(\chi_{765}(38, \cdot)\)	n/a	1280	4
765.4.bo	\(\chi_{765}(203, \cdot)\)	n/a	1280	4
765.4.bq	\(\chi_{765}(137, \cdot)\)	n/a	1152	4
765.4.bt	\(\chi_{765}(353, \cdot)\)	n/a	1280	4
765.4.bu	\(\chi_{765}(106, \cdot)\)	n/a	864	4
765.4.bx	\(\chi_{765}(73, \cdot)\)	n/a	1064	8
765.4.by	\(\chi_{765}(44, \cdot)\)	n/a	864	8
765.4.ca	\(\chi_{765}(71, \cdot)\)	n/a	576	8
765.4.cc	\(\chi_{765}(28, \cdot)\)	n/a	1064	8
765.4.cf	\(\chi_{765}(2, \cdot)\)	n/a	2560	8
765.4.cg	\(\chi_{765}(49, \cdot)\)	n/a	2560	8
765.4.cj	\(\chi_{765}(76, \cdot)\)	n/a	1728	8
765.4.ck	\(\chi_{765}(77, \cdot)\)	n/a	2560	8
765.4.cn	\(\chi_{765}(22, \cdot)\)	n/a	5120	16
765.4.cp	\(\chi_{765}(11, \cdot)\)	n/a	3456	16
765.4.cr	\(\chi_{765}(14, \cdot)\)	n/a	5120	16
765.4.cs	\(\chi_{765}(7, \cdot)\)	n/a	5120	16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(765))\) into lower level spaces

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