Space of modular forms of level 832 and weight 6

• Label: 832.6
• Level: 832
• Weight: 6
• Dimension: 59518
• Nonzero newspaces: 28
• Sturm bound: 258048
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(258048\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(832))\).

	Total	New	Old
Modular forms	108384	60002	48382
Cusp forms	106656	59518	47138
Eisenstein series	1728	484	1244

Trace form

59518 * q - 80 * q^2 - 60 * q^3 - 80 * q^4 - 80 * q^5 - 80 * q^6 - 56 * q^7 - 80 * q^8 + 386 * q^9 - 80 * q^10 - 1268 * q^11 - 80 * q^12 + 144 * q^13 - 176 * q^14 + 3536 * q^15 - 80 * q^16 + 1476 * q^17 - 80 * q^18 - 4780 * q^19 - 80 * q^20 - 10520 * q^21 - 27264 * q^22 - 56 * q^23 + 44000 * q^24 + 31078 * q^25 + 25872 * q^26 + 8304 * q^27 - 8800 * q^28 - 16368 * q^29 - 129840 * q^30 - 23144 * q^31 - 74400 * q^32 - 44464 * q^33 - 25600 * q^34 + 17216 * q^35 + 124560 * q^36 + 46816 * q^37 + 139200 * q^38 - 64 * q^39 + 124544 * q^40 - 26724 * q^41 - 92800 * q^42 - 30820 * q^43 - 131104 * q^44 + 46968 * q^45 - 80 * q^46 + 88296 * q^47 - 80 * q^48 + 24774 * q^49 + 274048 * q^50 - 89072 * q^51 - 73576 * q^52 - 77888 * q^53 - 466640 * q^54 + 440136 * q^55 - 301920 * q^56 - 70808 * q^57 - 52064 * q^58 - 175364 * q^59 + 395632 * q^60 + 100224 * q^61 + 350672 * q^62 - 659392 * q^63 + 749680 * q^64 - 14000 * q^65 + 509072 * q^66 - 395116 * q^67 + 14224 * q^68 - 287096 * q^69 - 573968 * q^70 + 575304 * q^71 - 828224 * q^72 + 169884 * q^73 - 755520 * q^74 + 1082388 * q^75 - 537040 * q^76 + 106472 * q^77 - 332752 * q^78 - 816576 * q^79 + 599648 * q^80 + 411118 * q^81 + 1006160 * q^82 + 455620 * q^83 + 1970000 * q^84 + 497888 * q^85 + 1443648 * q^86 - 56 * q^87 + 446480 * q^88 - 230468 * q^89 - 568880 * q^90 - 231228 * q^91 - 1842720 * q^92 - 722720 * q^93 - 1642640 * q^94 - 500832 * q^95 - 2428768 * q^96 - 1030604 * q^97 - 1914688 * q^98 - 597484 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(832))\)

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
832.6.a	\(\chi_{832}(1, \cdot)\)	832.6.a.a	1	1
		832.6.a.b	1
		832.6.a.c	1
		832.6.a.d	1
		832.6.a.e	1
		832.6.a.f	1
		832.6.a.g	1
		832.6.a.h	1
		832.6.a.i	2
		832.6.a.j	2
		832.6.a.k	2
		832.6.a.l	2
		832.6.a.m	2
		832.6.a.n	2
		832.6.a.o	2
		832.6.a.p	2
		832.6.a.q	3
		832.6.a.r	3
		832.6.a.s	3
		832.6.a.t	3
		832.6.a.u	3
		832.6.a.v	3
		832.6.a.w	4
		832.6.a.x	4
		832.6.a.y	5
		832.6.a.z	5
		832.6.a.ba	6
		832.6.a.bb	6
		832.6.a.bc	7
		832.6.a.bd	7
		832.6.a.be	8
		832.6.a.bf	8
		832.6.a.bg	8
		832.6.a.bh	10
832.6.b	\(\chi_{832}(417, \cdot)\)	n/a	120	1
832.6.e	\(\chi_{832}(545, \cdot)\)	n/a	140	1
832.6.f	\(\chi_{832}(129, \cdot)\)	n/a	138	1
832.6.i	\(\chi_{832}(321, \cdot)\)	n/a	276	2
832.6.k	\(\chi_{832}(255, \cdot)\)	n/a	276	2
832.6.l	\(\chi_{832}(239, \cdot)\)	n/a	276	2
832.6.n	\(\chi_{832}(209, \cdot)\)	n/a	240	2
832.6.p	\(\chi_{832}(337, \cdot)\)	n/a	276	2
832.6.s	\(\chi_{832}(47, \cdot)\)	n/a	276	2
832.6.u	\(\chi_{832}(31, \cdot)\)	n/a	280	2
832.6.w	\(\chi_{832}(257, \cdot)\)	n/a	276	2
832.6.z	\(\chi_{832}(289, \cdot)\)	n/a	280	2
832.6.ba	\(\chi_{832}(225, \cdot)\)	n/a	280	2
832.6.bd	\(\chi_{832}(343, \cdot)\)	None	0	4
832.6.bf	\(\chi_{832}(105, \cdot)\)	None	0	4
832.6.bg	\(\chi_{832}(25, \cdot)\)	None	0	4
832.6.bi	\(\chi_{832}(135, \cdot)\)	None	0	4
832.6.bk	\(\chi_{832}(223, \cdot)\)	n/a	560	4
832.6.bn	\(\chi_{832}(175, \cdot)\)	n/a	552	4
832.6.bp	\(\chi_{832}(17, \cdot)\)	n/a	552	4
832.6.br	\(\chi_{832}(81, \cdot)\)	n/a	552	4
832.6.bs	\(\chi_{832}(15, \cdot)\)	n/a	552	4
832.6.bu	\(\chi_{832}(63, \cdot)\)	n/a	552	4
832.6.bw	\(\chi_{832}(99, \cdot)\)	n/a	4464	8
832.6.by	\(\chi_{832}(53, \cdot)\)	n/a	3840	8
832.6.cb	\(\chi_{832}(77, \cdot)\)	n/a	4464	8
832.6.cc	\(\chi_{832}(83, \cdot)\)	n/a	4464	8
832.6.cf	\(\chi_{832}(71, \cdot)\)	None	0	8
832.6.ch	\(\chi_{832}(121, \cdot)\)	None	0	8
832.6.ci	\(\chi_{832}(9, \cdot)\)	None	0	8
832.6.ck	\(\chi_{832}(7, \cdot)\)	None	0	8
832.6.cn	\(\chi_{832}(11, \cdot)\)	n/a	8928	16
832.6.cp	\(\chi_{832}(29, \cdot)\)	n/a	8928	16
832.6.cq	\(\chi_{832}(69, \cdot)\)	n/a	8928	16
832.6.ct	\(\chi_{832}(115, \cdot)\)	n/a	8928	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(832))\) into lower level spaces

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