Space of modular forms of level 784 and weight 4

• Label: 784.4
• Level: 784
• Weight: 4
• Dimension: 30251
• Nonzero newspaces: 16
• Sturm bound: 150528
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(150528\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(784))\).

	Total	New	Old
Modular forms	57288	30688	26600
Cusp forms	55608	30251	25357
Eisenstein series	1680	437	1243

Trace form

30251 * q - 62 * q^2 - 43 * q^3 - 52 * q^4 - 79 * q^5 - 92 * q^6 - 54 * q^7 - 152 * q^8 - 26 * q^9 - 128 * q^10 + 17 * q^11 + 40 * q^12 - 49 * q^13 - 72 * q^14 - 213 * q^15 + 220 * q^16 - 89 * q^17 + 114 * q^18 + 425 * q^19 - 256 * q^20 + 90 * q^21 - 696 * q^22 - 241 * q^23 - 908 * q^24 - 1144 * q^25 - 324 * q^26 - 1315 * q^27 - 72 * q^28 - 739 * q^29 + 1176 * q^30 - 237 * q^31 + 908 * q^32 + 181 * q^33 + 376 * q^34 + 468 * q^35 - 704 * q^36 + 1265 * q^37 - 1292 * q^38 + 1141 * q^39 - 1396 * q^40 - 207 * q^41 - 2664 * q^42 - 2183 * q^43 - 6584 * q^44 - 4977 * q^45 - 3128 * q^46 - 2129 * q^47 + 1468 * q^48 + 462 * q^49 + 4734 * q^50 + 755 * q^51 + 8992 * q^52 + 4009 * q^53 + 16372 * q^54 + 2477 * q^55 + 4548 * q^56 + 9973 * q^57 + 8180 * q^58 + 4393 * q^59 + 11508 * q^60 + 3785 * q^61 + 2668 * q^62 - 84 * q^63 - 2452 * q^64 - 3281 * q^65 - 13688 * q^66 + 1205 * q^67 - 13060 * q^68 - 5361 * q^69 - 7512 * q^70 + 2227 * q^71 - 11256 * q^72 + 1435 * q^73 - 512 * q^74 - 5421 * q^75 - 1288 * q^76 - 2058 * q^77 - 880 * q^78 - 9097 * q^79 - 2708 * q^80 - 7194 * q^81 - 764 * q^82 - 11813 * q^83 - 72 * q^84 - 8023 * q^85 + 3704 * q^86 - 7083 * q^87 + 1468 * q^88 - 4389 * q^89 + 7020 * q^90 - 6333 * q^91 + 6980 * q^92 - 6499 * q^93 + 24772 * q^94 - 16745 * q^95 + 26468 * q^96 + 4120 * q^97 + 5892 * q^98 + 2134 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(784))\)

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
784.4.a	\(\chi_{784}(1, \cdot)\)	784.4.a.a	1	1
		784.4.a.b	1
		784.4.a.c	1
		784.4.a.d	1
		784.4.a.e	1
		784.4.a.f	1
		784.4.a.g	1
		784.4.a.h	1
		784.4.a.i	1
		784.4.a.j	1
		784.4.a.k	1
		784.4.a.l	1
		784.4.a.m	1
		784.4.a.n	1
		784.4.a.o	1
		784.4.a.p	1
		784.4.a.q	1
		784.4.a.r	1
		784.4.a.s	1
		784.4.a.t	2
		784.4.a.u	2
		784.4.a.v	2
		784.4.a.w	2
		784.4.a.x	2
		784.4.a.y	2
		784.4.a.z	2
		784.4.a.ba	2
		784.4.a.bb	3
		784.4.a.bc	3
		784.4.a.bd	3
		784.4.a.be	3
		784.4.a.bf	4
		784.4.a.bg	4
		784.4.a.bh	4
784.4.b	\(\chi_{784}(393, \cdot)\)	None	0	1
784.4.e	\(\chi_{784}(391, \cdot)\)	None	0	1
784.4.f	\(\chi_{784}(783, \cdot)\)	784.4.f.a	2	1
		784.4.f.b	2
		784.4.f.c	2
		784.4.f.d	2
		784.4.f.e	4
		784.4.f.f	4
		784.4.f.g	6
		784.4.f.h	6
		784.4.f.i	8
		784.4.f.j	24
784.4.i	\(\chi_{784}(177, \cdot)\)	n/a	116	2
784.4.j	\(\chi_{784}(195, \cdot)\)	n/a	472	2
784.4.m	\(\chi_{784}(197, \cdot)\)	n/a	482	2
784.4.p	\(\chi_{784}(31, \cdot)\)	n/a	120	2
784.4.q	\(\chi_{784}(215, \cdot)\)	None	0	2
784.4.t	\(\chi_{784}(361, \cdot)\)	None	0	2
784.4.u	\(\chi_{784}(113, \cdot)\)	n/a	498	6
784.4.w	\(\chi_{784}(19, \cdot)\)	n/a	944	4
784.4.x	\(\chi_{784}(165, \cdot)\)	n/a	944	4
784.4.bb	\(\chi_{784}(111, \cdot)\)	n/a	504	6
784.4.bc	\(\chi_{784}(55, \cdot)\)	None	0	6
784.4.bf	\(\chi_{784}(57, \cdot)\)	None	0	6
784.4.bg	\(\chi_{784}(65, \cdot)\)	n/a	996	12
784.4.bh	\(\chi_{784}(29, \cdot)\)	n/a	4008	12
784.4.bk	\(\chi_{784}(27, \cdot)\)	n/a	4008	12
784.4.bl	\(\chi_{784}(9, \cdot)\)	None	0	12
784.4.bo	\(\chi_{784}(87, \cdot)\)	None	0	12
784.4.bp	\(\chi_{784}(47, \cdot)\)	n/a	1008	12
784.4.bt	\(\chi_{784}(37, \cdot)\)	n/a	8016	24
784.4.bu	\(\chi_{784}(3, \cdot)\)	n/a	8016	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(784))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(784)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)