Space of modular forms of level 1976 and weight 2

• Label: 1976.2
• Level: 1976
• Weight: 2
• Dimension: 66108
• Nonzero newspaces: 72
• Sturm bound: 483840
• Trace bound: 24

Defining parameters

Level:	\( N \)	=	\( 1976 = 2^{3} \cdot 13 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(483840\)
Trace bound:			\(24\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1976))\).

	Total	New	Old
Modular forms	123552	67604	55948
Cusp forms	118369	66108	52261
Eisenstein series	5183	1496	3687

Trace form

66108 * q - 156 * q^2 - 156 * q^3 - 156 * q^4 - 156 * q^6 - 156 * q^7 - 156 * q^8 - 312 * q^9 - 156 * q^10 - 156 * q^11 - 156 * q^12 - 348 * q^14 - 156 * q^15 - 156 * q^16 - 306 * q^17 - 156 * q^18 - 156 * q^19 - 336 * q^20 + 48 * q^21 - 156 * q^22 - 132 * q^23 - 156 * q^24 - 282 * q^25 - 174 * q^26 - 258 * q^27 - 156 * q^28 + 66 * q^29 - 156 * q^30 - 96 * q^31 - 156 * q^32 - 156 * q^33 - 156 * q^34 - 60 * q^35 - 228 * q^36 + 42 * q^37 - 168 * q^38 - 342 * q^39 - 444 * q^40 - 294 * q^41 - 300 * q^42 - 180 * q^43 - 276 * q^44 + 18 * q^45 - 396 * q^46 - 192 * q^47 - 348 * q^48 - 300 * q^49 - 372 * q^50 - 306 * q^51 - 390 * q^52 - 72 * q^53 - 480 * q^54 - 300 * q^55 - 372 * q^56 - 348 * q^57 - 528 * q^58 - 228 * q^59 - 468 * q^60 - 126 * q^61 - 456 * q^62 - 348 * q^63 - 588 * q^64 - 348 * q^65 - 732 * q^66 - 348 * q^67 - 408 * q^68 + 72 * q^69 - 708 * q^70 - 168 * q^71 - 696 * q^72 - 378 * q^73 - 444 * q^74 - 396 * q^75 - 528 * q^76 - 12 * q^77 - 354 * q^78 - 552 * q^79 - 444 * q^80 - 378 * q^81 - 696 * q^82 - 144 * q^83 - 420 * q^84 + 78 * q^85 - 312 * q^86 - 420 * q^87 - 324 * q^88 - 420 * q^89 - 132 * q^90 - 390 * q^91 - 384 * q^92 - 108 * q^93 - 36 * q^94 - 192 * q^95 + 96 * q^96 - 312 * q^97 + 60 * q^98 - 414 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1976))\)

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
1976.2.a	\(\chi_{1976}(1, \cdot)\)	1976.2.a.a	1	1
		1976.2.a.b	1
		1976.2.a.c	2
		1976.2.a.d	3
		1976.2.a.e	4
		1976.2.a.f	4
		1976.2.a.g	5
		1976.2.a.h	7
		1976.2.a.i	7
		1976.2.a.j	10
		1976.2.a.k	10
1976.2.c	\(\chi_{1976}(1899, \cdot)\)	n/a	240	1
1976.2.d	\(\chi_{1976}(989, \cdot)\)	n/a	216	1
1976.2.g	\(\chi_{1976}(77, \cdot)\)	n/a	252	1
1976.2.h	\(\chi_{1976}(987, \cdot)\)	n/a	276	1
1976.2.j	\(\chi_{1976}(1065, \cdot)\)	1976.2.j.a	2	1
		1976.2.j.b	2
		1976.2.j.c	2
		1976.2.j.d	4
		1976.2.j.e	24
		1976.2.j.f	28
1976.2.m	\(\chi_{1976}(1975, \cdot)\)	None	0	1
1976.2.n	\(\chi_{1976}(911, \cdot)\)	None	0	1
1976.2.q	\(\chi_{1976}(1569, \cdot)\)	n/a	140	2
1976.2.r	\(\chi_{1976}(729, \cdot)\)	n/a	120	2
1976.2.s	\(\chi_{1976}(913, \cdot)\)	n/a	128	2
1976.2.t	\(\chi_{1976}(425, \cdot)\)	n/a	140	2
1976.2.v	\(\chi_{1976}(265, \cdot)\)	n/a	140	2
1976.2.w	\(\chi_{1976}(343, \cdot)\)	None	0	2
1976.2.y	\(\chi_{1976}(645, \cdot)\)	n/a	552	2
1976.2.bb	\(\chi_{1976}(723, \cdot)\)	n/a	504	2
1976.2.bd	\(\chi_{1976}(179, \cdot)\)	n/a	552	2
1976.2.be	\(\chi_{1976}(1037, \cdot)\)	n/a	552	2
1976.2.bh	\(\chi_{1976}(1413, \cdot)\)	n/a	552	2
1976.2.bi	\(\chi_{1976}(867, \cdot)\)	n/a	552	2
1976.2.bk	\(\chi_{1976}(303, \cdot)\)	None	0	2
1976.2.bn	\(\chi_{1976}(153, \cdot)\)	n/a	124	2
1976.2.bo	\(\chi_{1976}(183, \cdot)\)	None	0	2
1976.2.bs	\(\chi_{1976}(711, \cdot)\)	None	0	2
1976.2.bu	\(\chi_{1976}(961, \cdot)\)	n/a	140	2
1976.2.bw	\(\chi_{1976}(335, \cdot)\)	None	0	2
1976.2.bz	\(\chi_{1976}(881, \cdot)\)	n/a	140	2
1976.2.cb	\(\chi_{1976}(103, \cdot)\)	None	0	2
1976.2.ce	\(\chi_{1976}(607, \cdot)\)	None	0	2
1976.2.cg	\(\chi_{1976}(685, \cdot)\)	n/a	504	2
1976.2.ch	\(\chi_{1976}(835, \cdot)\)	n/a	552	2
1976.2.ck	\(\chi_{1976}(805, \cdot)\)	n/a	552	2
1976.2.cm	\(\chi_{1976}(1323, \cdot)\)	n/a	552	2
1976.2.cn	\(\chi_{1976}(277, \cdot)\)	n/a	552	2
1976.2.cp	\(\chi_{1976}(259, \cdot)\)	n/a	552	2
1976.2.cs	\(\chi_{1976}(27, \cdot)\)	n/a	480	2
1976.2.cu	\(\chi_{1976}(581, \cdot)\)	n/a	552	2
1976.2.cv	\(\chi_{1976}(107, \cdot)\)	n/a	552	2
1976.2.cx	\(\chi_{1976}(885, \cdot)\)	n/a	480	2
1976.2.da	\(\chi_{1976}(75, \cdot)\)	n/a	552	2
1976.2.db	\(\chi_{1976}(381, \cdot)\)	n/a	504	2
1976.2.df	\(\chi_{1976}(1855, \cdot)\)	None	0	2
1976.2.dg	\(\chi_{1976}(1167, \cdot)\)	None	0	2
1976.2.dj	\(\chi_{1976}(49, \cdot)\)	n/a	140	2
1976.2.dk	\(\chi_{1976}(289, \cdot)\)	n/a	420	6
1976.2.dl	\(\chi_{1976}(313, \cdot)\)	n/a	360	6
1976.2.dm	\(\chi_{1976}(9, \cdot)\)	n/a	420	6
1976.2.do	\(\chi_{1976}(7, \cdot)\)	None	0	4
1976.2.dp	\(\chi_{1976}(449, \cdot)\)	n/a	280	4
1976.2.dr	\(\chi_{1976}(293, \cdot)\)	n/a	1104	4
1976.2.du	\(\chi_{1976}(163, \cdot)\)	n/a	1104	4
1976.2.dv	\(\chi_{1976}(115, \cdot)\)	n/a	1008	4
1976.2.dx	\(\chi_{1976}(83, \cdot)\)	n/a	1104	4
1976.2.ea	\(\chi_{1976}(37, \cdot)\)	n/a	1104	4
1976.2.ec	\(\chi_{1976}(525, \cdot)\)	n/a	1104	4
1976.2.ee	\(\chi_{1976}(145, \cdot)\)	n/a	280	4
1976.2.ef	\(\chi_{1976}(695, \cdot)\)	None	0	4
1976.2.ei	\(\chi_{1976}(799, \cdot)\)	None	0	4
1976.2.ek	\(\chi_{1976}(239, \cdot)\)	None	0	4
1976.2.el	\(\chi_{1976}(721, \cdot)\)	n/a	280	4
1976.2.en	\(\chi_{1976}(369, \cdot)\)	n/a	280	4
1976.2.ep	\(\chi_{1976}(11, \cdot)\)	n/a	1104	4
1976.2.es	\(\chi_{1976}(141, \cdot)\)	n/a	1104	4
1976.2.et	\(\chi_{1976}(295, \cdot)\)	None	0	6
1976.2.eu	\(\chi_{1976}(329, \cdot)\)	n/a	420	6
1976.2.ez	\(\chi_{1976}(3, \cdot)\)	n/a	1656	6
1976.2.fa	\(\chi_{1976}(309, \cdot)\)	n/a	1656	6
1976.2.fb	\(\chi_{1976}(127, \cdot)\)	None	0	6
1976.2.fc	\(\chi_{1976}(623, \cdot)\)	None	0	6
1976.2.fl	\(\chi_{1976}(157, \cdot)\)	n/a	1440	6
1976.2.fm	\(\chi_{1976}(237, \cdot)\)	n/a	1656	6
1976.2.fn	\(\chi_{1976}(51, \cdot)\)	n/a	1656	6
1976.2.fo	\(\chi_{1976}(147, \cdot)\)	n/a	1656	6
1976.2.ft	\(\chi_{1976}(451, \cdot)\)	n/a	1656	6
1976.2.fu	\(\chi_{1976}(547, \cdot)\)	n/a	1440	6
1976.2.fv	\(\chi_{1976}(101, \cdot)\)	n/a	1656	6
1976.2.fw	\(\chi_{1976}(389, \cdot)\)	n/a	1656	6
1976.2.fx	\(\chi_{1976}(79, \cdot)\)	None	0	6
1976.2.fy	\(\chi_{1976}(471, \cdot)\)	None	0	6
1976.2.fz	\(\chi_{1976}(25, \cdot)\)	n/a	420	6
1976.2.ga	\(\chi_{1976}(17, \cdot)\)	n/a	420	6
1976.2.gh	\(\chi_{1976}(61, \cdot)\)	n/a	1656	6
1976.2.gi	\(\chi_{1976}(355, \cdot)\)	n/a	1656	6
1976.2.gj	\(\chi_{1976}(231, \cdot)\)	None	0	6
1976.2.gn	\(\chi_{1976}(357, \cdot)\)	n/a	3312	12
1976.2.gp	\(\chi_{1976}(123, \cdot)\)	n/a	3312	12
1976.2.gr	\(\chi_{1976}(99, \cdot)\)	n/a	3312	12
1976.2.gt	\(\chi_{1976}(275, \cdot)\)	n/a	3312	12
1976.2.gv	\(\chi_{1976}(21, \cdot)\)	n/a	3312	12
1976.2.gx	\(\chi_{1976}(509, \cdot)\)	n/a	3312	12
1976.2.gy	\(\chi_{1976}(119, \cdot)\)	None	0	12
1976.2.ha	\(\chi_{1976}(41, \cdot)\)	n/a	840	12
1976.2.hc	\(\chi_{1976}(33, \cdot)\)	n/a	840	12
1976.2.he	\(\chi_{1976}(281, \cdot)\)	n/a	840	12
1976.2.hg	\(\chi_{1976}(63, \cdot)\)	None	0	12
1976.2.hi	\(\chi_{1976}(47, \cdot)\)	None	0	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1976))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1976)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(494))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(988))\)\(^{\oplus 2}\)