Space of modular forms of level 832 and weight 3

• Label: 832.3
• Level: 832
• Weight: 3
• Dimension: 23662
• Nonzero newspaces: 28
• Sturm bound: 129024
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(129024\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(832))\).

	Total	New	Old
Modular forms	43872	24146	19726
Cusp forms	42144	23662	18482
Eisenstein series	1728	484	1244

Trace form

23662 * q - 80 * q^2 - 60 * q^3 - 80 * q^4 - 80 * q^5 - 80 * q^6 - 64 * q^7 - 80 * q^8 - 118 * q^9 - 80 * q^10 - 92 * q^11 - 80 * q^12 - 104 * q^13 - 176 * q^14 - 56 * q^15 - 80 * q^16 - 108 * q^17 - 80 * q^18 + 4 * q^19 - 80 * q^20 + 88 * q^21 + 64 * q^22 + 64 * q^23 + 480 * q^24 + 142 * q^25 + 112 * q^26 + 160 * q^28 - 16 * q^29 + 80 * q^30 - 40 * q^31 - 160 * q^32 - 224 * q^33 - 320 * q^34 - 256 * q^35 - 880 * q^36 - 432 * q^37 - 640 * q^38 - 260 * q^39 - 896 * q^40 - 612 * q^41 - 960 * q^42 - 284 * q^43 - 288 * q^44 - 376 * q^45 - 80 * q^46 - 56 * q^47 - 80 * q^48 + 22 * q^49 - 704 * q^50 + 1024 * q^51 - 616 * q^52 + 112 * q^53 - 1232 * q^54 + 1472 * q^55 - 864 * q^56 + 376 * q^57 - 800 * q^58 + 868 * q^59 - 656 * q^60 + 144 * q^61 - 112 * q^62 - 72 * q^63 + 112 * q^64 - 336 * q^65 + 336 * q^66 - 1148 * q^67 + 400 * q^68 - 488 * q^69 + 1264 * q^70 - 1600 * q^71 + 1216 * q^72 - 612 * q^73 + 1152 * q^74 - 2068 * q^75 + 1584 * q^76 + 216 * q^77 + 1040 * q^78 - 1152 * q^79 + 2656 * q^80 + 686 * q^81 + 2000 * q^82 + 580 * q^83 + 2384 * q^84 + 848 * q^85 + 1792 * q^86 + 832 * q^87 + 1040 * q^88 + 988 * q^89 + 1360 * q^90 + 124 * q^91 + 736 * q^92 + 640 * q^93 + 112 * q^94 - 40 * q^95 - 352 * q^96 - 476 * q^97 - 896 * q^98 - 652 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(832))\)

We only show spaces with odd 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
832.3.c	\(\chi_{832}(831, \cdot)\)	832.3.c.a	1	1
		832.3.c.b	1
		832.3.c.c	2
		832.3.c.d	2
		832.3.c.e	4
		832.3.c.f	8
		832.3.c.g	8
		832.3.c.h	14
		832.3.c.i	14
832.3.d	\(\chi_{832}(703, \cdot)\)	832.3.d.a	4	1
		832.3.d.b	8
		832.3.d.c	12
		832.3.d.d	12
		832.3.d.e	12
832.3.g	\(\chi_{832}(287, \cdot)\)	832.3.g.a	16	1
		832.3.g.b	32
832.3.h	\(\chi_{832}(415, \cdot)\)	832.3.h.a	16	1
		832.3.h.b	40
832.3.j	\(\chi_{832}(161, \cdot)\)	n/a	112	2
832.3.m	\(\chi_{832}(177, \cdot)\)	n/a	108	2
832.3.o	\(\chi_{832}(207, \cdot)\)	n/a	108	2
832.3.q	\(\chi_{832}(79, \cdot)\)	832.3.q.a	96	2
832.3.r	\(\chi_{832}(369, \cdot)\)	n/a	108	2
832.3.t	\(\chi_{832}(385, \cdot)\)	n/a	108	2
832.3.v	\(\chi_{832}(159, \cdot)\)	n/a	112	2
832.3.x	\(\chi_{832}(95, \cdot)\)	n/a	112	2
832.3.y	\(\chi_{832}(127, \cdot)\)	n/a	108	2
832.3.bb	\(\chi_{832}(191, \cdot)\)	n/a	108	2
832.3.bc	\(\chi_{832}(57, \cdot)\)	None	0	4
832.3.be	\(\chi_{832}(103, \cdot)\)	None	0	4
832.3.bh	\(\chi_{832}(183, \cdot)\)	None	0	4
832.3.bj	\(\chi_{832}(265, \cdot)\)	None	0	4
832.3.bl	\(\chi_{832}(193, \cdot)\)	n/a	216	4
832.3.bm	\(\chi_{832}(145, \cdot)\)	n/a	216	4
832.3.bo	\(\chi_{832}(367, \cdot)\)	n/a	216	4
832.3.bq	\(\chi_{832}(303, \cdot)\)	n/a	216	4
832.3.bt	\(\chi_{832}(305, \cdot)\)	n/a	216	4
832.3.bv	\(\chi_{832}(33, \cdot)\)	n/a	224	4
832.3.bx	\(\chi_{832}(21, \cdot)\)	n/a	1776	8
832.3.bz	\(\chi_{832}(51, \cdot)\)	n/a	1776	8
832.3.ca	\(\chi_{832}(27, \cdot)\)	n/a	1536	8
832.3.cd	\(\chi_{832}(5, \cdot)\)	n/a	1776	8
832.3.ce	\(\chi_{832}(41, \cdot)\)	None	0	8
832.3.cg	\(\chi_{832}(55, \cdot)\)	None	0	8
832.3.cj	\(\chi_{832}(23, \cdot)\)	None	0	8
832.3.cl	\(\chi_{832}(137, \cdot)\)	None	0	8
832.3.cm	\(\chi_{832}(141, \cdot)\)	n/a	3552	16
832.3.co	\(\chi_{832}(43, \cdot)\)	n/a	3552	16
832.3.cr	\(\chi_{832}(3, \cdot)\)	n/a	3552	16
832.3.cs	\(\chi_{832}(37, \cdot)\)	n/a	3552	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(832))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(832)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)