Space of modular forms of level 704 and weight 6

• Label: 704.6
• Level: 704
• Weight: 6
• Dimension: 42282
• Nonzero newspaces: 16
• Sturm bound: 184320
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(184320\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(704))\).

	Total	New	Old
Modular forms	77520	42678	34842
Cusp forms	76080	42282	33798
Eisenstein series	1440	396	1044

Trace form

42282 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 44 * q^7 - 64 * q^8 + 406 * q^9 - 64 * q^10 - 658 * q^11 - 144 * q^12 + 400 * q^13 - 64 * q^14 + 3548 * q^15 - 64 * q^16 + 1504 * q^17 - 64 * q^18 - 4768 * q^19 - 64 * q^20 - 10504 * q^21 - 13664 * q^22 - 104 * q^23 + 44016 * q^24 + 31098 * q^25 + 51856 * q^26 + 8388 * q^27 - 8784 * q^28 - 16352 * q^29 - 129824 * q^30 - 23132 * q^31 - 74384 * q^32 - 22256 * q^33 - 25664 * q^34 + 17228 * q^35 + 124576 * q^36 + 46832 * q^37 + 139216 * q^38 - 44 * q^39 + 124656 * q^40 - 26704 * q^41 - 92784 * q^42 - 30808 * q^43 - 65584 * q^44 + 46904 * q^45 - 64 * q^46 + 88308 * q^47 - 64 * q^48 + 24802 * q^49 + 274064 * q^50 - 89060 * q^51 - 147040 * q^52 - 77776 * q^53 - 466624 * q^54 + 220044 * q^55 - 301984 * q^56 - 70788 * q^57 - 52048 * q^58 - 175352 * q^59 + 395648 * q^60 + 100240 * q^61 + 350688 * q^62 - 659380 * q^63 + 749696 * q^64 - 27692 * q^65 + 254552 * q^66 - 395164 * q^67 + 14240 * q^68 - 287080 * q^69 - 573952 * q^70 + 575316 * q^71 - 828208 * q^72 + 169904 * q^73 - 755504 * q^74 + 1082400 * q^75 - 537024 * q^76 + 53204 * q^77 - 665472 * q^78 - 816492 * q^79 + 599664 * q^80 + 411146 * q^81 + 1006176 * q^82 + 455632 * q^83 + 1970016 * q^84 + 497904 * q^85 + 1443664 * q^86 - 64 * q^87 + 223208 * q^88 - 230548 * q^89 - 568864 * q^90 - 462372 * q^91 - 1842608 * q^92 - 722704 * q^93 - 1642624 * q^94 - 500820 * q^95 - 2428752 * q^96 - 1030592 * q^97 - 1914672 * q^98 - 298766 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(704))\)

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
704.6.a	\(\chi_{704}(1, \cdot)\)	704.6.a.a	1	1
		704.6.a.b	1
		704.6.a.c	1
		704.6.a.d	1
		704.6.a.e	1
		704.6.a.f	1
		704.6.a.g	1
		704.6.a.h	1
		704.6.a.i	1
		704.6.a.j	1
		704.6.a.k	2
		704.6.a.l	2
		704.6.a.m	2
		704.6.a.n	2
		704.6.a.o	2
		704.6.a.p	2
		704.6.a.q	3
		704.6.a.r	3
		704.6.a.s	3
		704.6.a.t	3
		704.6.a.u	4
		704.6.a.v	4
		704.6.a.w	4
		704.6.a.x	4
		704.6.a.y	6
		704.6.a.z	6
		704.6.a.ba	6
		704.6.a.bb	6
		704.6.a.bc	6
		704.6.a.bd	6
		704.6.a.be	7
		704.6.a.bf	7
704.6.c	\(\chi_{704}(353, \cdot)\)	704.6.c.a	16	1
		704.6.c.b	20
		704.6.c.c	28
		704.6.c.d	36
704.6.e	\(\chi_{704}(703, \cdot)\)	n/a	118	1
704.6.g	\(\chi_{704}(351, \cdot)\)	n/a	120	1
704.6.i	\(\chi_{704}(175, \cdot)\)	n/a	236	2
704.6.j	\(\chi_{704}(177, \cdot)\)	n/a	200	2
704.6.m	\(\chi_{704}(257, \cdot)\)	n/a	472	4
704.6.n	\(\chi_{704}(89, \cdot)\)	None	0	4
704.6.q	\(\chi_{704}(87, \cdot)\)	None	0	4
704.6.s	\(\chi_{704}(95, \cdot)\)	n/a	480	4
704.6.u	\(\chi_{704}(63, \cdot)\)	n/a	472	4
704.6.w	\(\chi_{704}(97, \cdot)\)	n/a	480	4
704.6.z	\(\chi_{704}(45, \cdot)\)	n/a	3200	8
704.6.bb	\(\chi_{704}(43, \cdot)\)	n/a	3824	8
704.6.be	\(\chi_{704}(49, \cdot)\)	n/a	944	8
704.6.bf	\(\chi_{704}(79, \cdot)\)	n/a	944	8
704.6.bg	\(\chi_{704}(7, \cdot)\)	None	0	16
704.6.bj	\(\chi_{704}(9, \cdot)\)	None	0	16
704.6.bk	\(\chi_{704}(19, \cdot)\)	n/a	15296	32
704.6.bm	\(\chi_{704}(5, \cdot)\)	n/a	15296	32

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(704))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(704)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 1}\)