Space of modular forms of level 832 and weight 4

• Label: 832.4
• Level: 832
• Weight: 4
• Dimension: 35614
• Nonzero newspaces: 28
• Sturm bound: 172032
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(172032\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(832))\).

	Total	New	Old
Modular forms	65376	36098	29278
Cusp forms	63648	35614	28034
Eisenstein series	1728	484	1244

Trace form

35614 * q - 80 * q^2 - 60 * q^3 - 80 * q^4 - 80 * q^5 - 80 * q^6 - 56 * q^7 - 80 * q^8 - 46 * q^9 - 80 * q^10 - 20 * q^11 - 80 * q^12 - 160 * q^13 - 176 * q^14 - 304 * q^15 - 80 * q^16 - 348 * q^17 - 80 * q^18 - 108 * q^19 - 80 * q^20 - 56 * q^21 - 1024 * q^22 - 56 * q^23 - 2080 * q^24 - 202 * q^25 - 48 * q^26 + 240 * q^27 + 1440 * q^28 + 720 * q^29 + 4560 * q^30 + 664 * q^31 + 2400 * q^32 + 1904 * q^33 + 1920 * q^34 + 896 * q^35 + 1680 * q^36 + 960 * q^37 - 960 * q^38 - 64 * q^39 - 3456 * q^40 - 2148 * q^41 - 6400 * q^42 - 1732 * q^43 - 2080 * q^44 - 3048 * q^45 - 80 * q^46 - 1944 * q^47 - 80 * q^48 - 2266 * q^49 + 5632 * q^50 - 9008 * q^51 + 3224 * q^52 - 992 * q^53 + 3376 * q^54 - 1208 * q^55 - 864 * q^56 + 2056 * q^57 - 4832 * q^58 + 8860 * q^59 - 9872 * q^60 + 2080 * q^61 - 6064 * q^62 + 15296 * q^63 - 12176 * q^64 + 2032 * q^65 - 11248 * q^66 + 11988 * q^67 - 4208 * q^68 + 1192 * q^69 - 4112 * q^70 + 840 * q^71 + 1216 * q^72 - 2148 * q^73 + 5184 * q^74 - 14796 * q^75 + 11824 * q^76 - 6328 * q^77 + 1904 * q^78 - 20288 * q^79 - 8608 * q^80 - 13778 * q^81 - 14000 * q^82 - 5180 * q^83 - 8368 * q^84 - 3392 * q^85 + 960 * q^86 - 56 * q^87 + 6160 * q^88 + 7036 * q^89 + 18640 * q^90 + 3268 * q^91 + 25056 * q^92 + 16672 * q^93 + 17776 * q^94 + 13728 * q^95 + 25760 * q^96 + 18644 * q^97 + 24128 * q^98 + 9428 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(832))\)

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
832.4.a	\(\chi_{832}(1, \cdot)\)	832.4.a.a	1	1
		832.4.a.b	1
		832.4.a.c	1
		832.4.a.d	1
		832.4.a.e	1
		832.4.a.f	1
		832.4.a.g	1
		832.4.a.h	1
		832.4.a.i	1
		832.4.a.j	1
		832.4.a.k	1
		832.4.a.l	1
		832.4.a.m	1
		832.4.a.n	1
		832.4.a.o	1
		832.4.a.p	1
		832.4.a.q	1
		832.4.a.r	1
		832.4.a.s	2
		832.4.a.t	2
		832.4.a.u	2
		832.4.a.v	2
		832.4.a.w	2
		832.4.a.x	2
		832.4.a.y	2
		832.4.a.z	2
		832.4.a.ba	3
		832.4.a.bb	3
		832.4.a.bc	3
		832.4.a.bd	3
		832.4.a.be	4
		832.4.a.bf	5
		832.4.a.bg	5
		832.4.a.bh	6
		832.4.a.bi	6
832.4.b	\(\chi_{832}(417, \cdot)\)	832.4.b.a	12	1
		832.4.b.b	12
		832.4.b.c	24
		832.4.b.d	24
832.4.e	\(\chi_{832}(545, \cdot)\)	832.4.e.a	4	1
		832.4.e.b	8
		832.4.e.c	8
		832.4.e.d	8
		832.4.e.e	56
832.4.f	\(\chi_{832}(129, \cdot)\)	832.4.f.a	2	1
		832.4.f.b	2
		832.4.f.c	2
		832.4.f.d	2
		832.4.f.e	2
		832.4.f.f	2
		832.4.f.g	2
		832.4.f.h	4
		832.4.f.i	4
		832.4.f.j	4
		832.4.f.k	10
		832.4.f.l	10
		832.4.f.m	16
		832.4.f.n	20
832.4.i	\(\chi_{832}(321, \cdot)\)	n/a	164	2
832.4.k	\(\chi_{832}(255, \cdot)\)	n/a	164	2
832.4.l	\(\chi_{832}(239, \cdot)\)	n/a	164	2
832.4.n	\(\chi_{832}(209, \cdot)\)	n/a	144	2
832.4.p	\(\chi_{832}(337, \cdot)\)	n/a	164	2
832.4.s	\(\chi_{832}(47, \cdot)\)	n/a	164	2
832.4.u	\(\chi_{832}(31, \cdot)\)	n/a	168	2
832.4.w	\(\chi_{832}(257, \cdot)\)	n/a	164	2
832.4.z	\(\chi_{832}(289, \cdot)\)	n/a	168	2
832.4.ba	\(\chi_{832}(225, \cdot)\)	n/a	168	2
832.4.bd	\(\chi_{832}(343, \cdot)\)	None	0	4
832.4.bf	\(\chi_{832}(105, \cdot)\)	None	0	4
832.4.bg	\(\chi_{832}(25, \cdot)\)	None	0	4
832.4.bi	\(\chi_{832}(135, \cdot)\)	None	0	4
832.4.bk	\(\chi_{832}(223, \cdot)\)	n/a	336	4
832.4.bn	\(\chi_{832}(175, \cdot)\)	n/a	328	4
832.4.bp	\(\chi_{832}(17, \cdot)\)	n/a	328	4
832.4.br	\(\chi_{832}(81, \cdot)\)	n/a	328	4
832.4.bs	\(\chi_{832}(15, \cdot)\)	n/a	328	4
832.4.bu	\(\chi_{832}(63, \cdot)\)	n/a	328	4
832.4.bw	\(\chi_{832}(99, \cdot)\)	n/a	2672	8
832.4.by	\(\chi_{832}(53, \cdot)\)	n/a	2304	8
832.4.cb	\(\chi_{832}(77, \cdot)\)	n/a	2672	8
832.4.cc	\(\chi_{832}(83, \cdot)\)	n/a	2672	8
832.4.cf	\(\chi_{832}(71, \cdot)\)	None	0	8
832.4.ch	\(\chi_{832}(121, \cdot)\)	None	0	8
832.4.ci	\(\chi_{832}(9, \cdot)\)	None	0	8
832.4.ck	\(\chi_{832}(7, \cdot)\)	None	0	8
832.4.cn	\(\chi_{832}(11, \cdot)\)	n/a	5344	16
832.4.cp	\(\chi_{832}(29, \cdot)\)	n/a	5344	16
832.4.cq	\(\chi_{832}(69, \cdot)\)	n/a	5344	16
832.4.ct	\(\chi_{832}(115, \cdot)\)	n/a	5344	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(832))\) into lower level spaces

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