Space of modular forms of level 704 and weight 4

• Label: 704.4
• Level: 704
• Weight: 4
• Dimension: 25290
• Nonzero newspaces: 16
• Sturm bound: 122880
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(122880\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(704))\).

	Total	New	Old
Modular forms	46800	25686	21114
Cusp forms	45360	25290	20070
Eisenstein series	1440	396	1044

Trace form

25290 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 44 * q^7 - 64 * q^8 - 26 * q^9 - 64 * q^10 - 34 * q^11 - 144 * q^12 - 208 * q^13 - 64 * q^14 - 292 * q^15 - 64 * q^16 - 320 * q^17 - 64 * q^18 - 96 * q^19 - 64 * q^20 - 40 * q^21 - 544 * q^22 - 104 * q^23 - 2064 * q^24 - 182 * q^25 + 16 * q^26 + 324 * q^27 + 1456 * q^28 + 736 * q^29 + 4576 * q^30 + 676 * q^31 + 2416 * q^32 + 928 * q^33 + 1856 * q^34 + 908 * q^35 + 1696 * q^36 + 976 * q^37 - 944 * q^38 - 44 * q^39 - 3344 * q^40 - 2128 * q^41 - 6384 * q^42 - 1720 * q^43 - 1072 * q^44 - 3112 * q^45 - 64 * q^46 - 1932 * q^47 - 64 * q^48 - 2238 * q^49 + 5648 * q^50 - 8996 * q^51 + 6560 * q^52 - 880 * q^53 + 3392 * q^54 - 628 * q^55 - 928 * q^56 + 2076 * q^57 - 4816 * q^58 + 8872 * q^59 - 9856 * q^60 + 2096 * q^61 - 6048 * q^62 + 15308 * q^63 - 12160 * q^64 + 4372 * q^65 - 5608 * q^66 + 11940 * q^67 - 4192 * q^68 + 1208 * q^69 - 4096 * q^70 + 852 * q^71 + 1232 * q^72 - 2128 * q^73 + 5200 * q^74 - 14784 * q^75 + 11840 * q^76 - 3196 * q^77 + 3840 * q^78 - 20204 * q^79 - 8592 * q^80 - 13750 * q^81 - 13984 * q^82 - 5168 * q^83 - 8352 * q^84 - 3376 * q^85 + 976 * q^86 - 64 * q^87 + 3048 * q^88 + 6956 * q^89 + 18656 * q^90 + 6620 * q^91 + 25168 * q^92 + 16688 * q^93 + 17792 * q^94 + 13740 * q^95 + 25776 * q^96 + 18656 * q^97 + 24144 * q^98 + 4690 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(704))\)

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
704.4.a	\(\chi_{704}(1, \cdot)\)	704.4.a.a	1	1
		704.4.a.b	1
		704.4.a.c	1
		704.4.a.d	1
		704.4.a.e	1
		704.4.a.f	1
		704.4.a.g	1
		704.4.a.h	1
		704.4.a.i	1
		704.4.a.j	1
		704.4.a.k	1
		704.4.a.l	1
		704.4.a.m	2
		704.4.a.n	2
		704.4.a.o	2
		704.4.a.p	2
		704.4.a.q	2
		704.4.a.r	2
		704.4.a.s	3
		704.4.a.t	3
		704.4.a.u	3
		704.4.a.v	3
		704.4.a.w	4
		704.4.a.x	4
		704.4.a.y	4
		704.4.a.z	4
		704.4.a.ba	4
		704.4.a.bb	4
704.4.c	\(\chi_{704}(353, \cdot)\)	704.4.c.a	4	1
		704.4.c.b	4
		704.4.c.c	12
		704.4.c.d	16
		704.4.c.e	24
704.4.e	\(\chi_{704}(703, \cdot)\)	704.4.e.a	2	1
		704.4.e.b	2
		704.4.e.c	2
		704.4.e.d	4
		704.4.e.e	8
		704.4.e.f	16
		704.4.e.g	36
704.4.g	\(\chi_{704}(351, \cdot)\)	704.4.g.a	4	1
		704.4.g.b	4
		704.4.g.c	8
		704.4.g.d	16
		704.4.g.e	40
704.4.i	\(\chi_{704}(175, \cdot)\)	n/a	140	2
704.4.j	\(\chi_{704}(177, \cdot)\)	n/a	120	2
704.4.m	\(\chi_{704}(257, \cdot)\)	n/a	280	4
704.4.n	\(\chi_{704}(89, \cdot)\)	None	0	4
704.4.q	\(\chi_{704}(87, \cdot)\)	None	0	4
704.4.s	\(\chi_{704}(95, \cdot)\)	n/a	288	4
704.4.u	\(\chi_{704}(63, \cdot)\)	n/a	280	4
704.4.w	\(\chi_{704}(97, \cdot)\)	n/a	288	4
704.4.z	\(\chi_{704}(45, \cdot)\)	n/a	1920	8
704.4.bb	\(\chi_{704}(43, \cdot)\)	n/a	2288	8
704.4.be	\(\chi_{704}(49, \cdot)\)	n/a	560	8
704.4.bf	\(\chi_{704}(79, \cdot)\)	n/a	560	8
704.4.bg	\(\chi_{704}(7, \cdot)\)	None	0	16
704.4.bj	\(\chi_{704}(9, \cdot)\)	None	0	16
704.4.bk	\(\chi_{704}(19, \cdot)\)	n/a	9152	32
704.4.bm	\(\chi_{704}(5, \cdot)\)	n/a	9152	32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(704))\) into lower level spaces

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