Space of modular forms of level 1984 and weight 2

• Label: 1984.2
• Level: 1984
• Weight: 2
• Dimension: 68338
• Nonzero newspaces: 32
• Sturm bound: 491520
• Trace bound: 49

Defining parameters

Level:	\( N \)	=	\( 1984 = 2^{6} \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(491520\)
Trace bound:			\(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1984))\).

	Total	New	Old
Modular forms	125040	69614	55426
Cusp forms	120721	68338	52383
Eisenstein series	4319	1276	3043

Trace form

68338 * q - 224 * q^2 - 168 * q^3 - 224 * q^4 - 224 * q^5 - 224 * q^6 - 164 * q^7 - 224 * q^8 - 274 * q^9 - 224 * q^10 - 160 * q^11 - 224 * q^12 - 208 * q^13 - 224 * q^14 - 156 * q^15 - 224 * q^16 - 376 * q^17 - 224 * q^18 - 152 * q^19 - 224 * q^20 - 232 * q^21 - 240 * q^22 - 164 * q^23 - 304 * q^24 - 302 * q^25 - 304 * q^26 - 180 * q^27 - 304 * q^28 - 256 * q^29 - 384 * q^30 - 196 * q^31 - 544 * q^32 - 220 * q^33 - 304 * q^34 - 172 * q^35 - 384 * q^36 - 240 * q^37 - 304 * q^38 - 164 * q^39 - 304 * q^40 - 280 * q^41 - 304 * q^42 - 144 * q^43 - 240 * q^44 - 216 * q^45 - 224 * q^46 - 132 * q^47 - 224 * q^48 - 374 * q^49 - 176 * q^50 - 220 * q^51 - 128 * q^52 - 176 * q^53 - 96 * q^54 - 292 * q^55 - 112 * q^56 - 268 * q^57 - 80 * q^58 - 304 * q^59 - 32 * q^60 - 208 * q^61 - 200 * q^62 - 480 * q^63 - 32 * q^64 - 612 * q^65 - 64 * q^66 - 344 * q^67 - 128 * q^68 - 200 * q^69 - 32 * q^70 - 292 * q^71 - 80 * q^72 - 280 * q^73 - 112 * q^74 - 280 * q^75 - 96 * q^76 - 232 * q^77 - 176 * q^78 - 228 * q^79 - 304 * q^80 - 398 * q^81 - 384 * q^82 - 168 * q^83 - 448 * q^84 - 240 * q^85 - 432 * q^86 - 164 * q^87 - 384 * q^88 - 376 * q^89 - 512 * q^90 - 156 * q^91 - 528 * q^92 - 272 * q^93 - 656 * q^94 - 204 * q^95 - 496 * q^96 - 248 * q^97 - 496 * q^98 - 216 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1984))\)

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
1984.2.a	\(\chi_{1984}(1, \cdot)\)	1984.2.a.a	1	1
		1984.2.a.b	1
		1984.2.a.c	1
		1984.2.a.d	1
		1984.2.a.e	1
		1984.2.a.f	1
		1984.2.a.g	1
		1984.2.a.h	1
		1984.2.a.i	1
		1984.2.a.j	1
		1984.2.a.k	1
		1984.2.a.l	1
		1984.2.a.m	2
		1984.2.a.n	2
		1984.2.a.o	2
		1984.2.a.p	2
		1984.2.a.q	2
		1984.2.a.r	2
		1984.2.a.s	2
		1984.2.a.t	2
		1984.2.a.u	3
		1984.2.a.v	3
		1984.2.a.w	3
		1984.2.a.x	3
		1984.2.a.y	4
		1984.2.a.z	4
		1984.2.a.ba	6
		1984.2.a.bb	6
1984.2.b	\(\chi_{1984}(991, \cdot)\)	1984.2.b.a	8	1
		1984.2.b.b	16
		1984.2.b.c	40
1984.2.c	\(\chi_{1984}(993, \cdot)\)	1984.2.c.a	4	1
		1984.2.c.b	4
		1984.2.c.c	6
		1984.2.c.d	6
		1984.2.c.e	20
		1984.2.c.f	20
1984.2.h	\(\chi_{1984}(1983, \cdot)\)	1984.2.h.a	2	1
		1984.2.h.b	2
		1984.2.h.c	4
		1984.2.h.d	4
		1984.2.h.e	4
		1984.2.h.f	6
		1984.2.h.g	8
		1984.2.h.h	32
1984.2.i	\(\chi_{1984}(129, \cdot)\)	n/a	124	2
1984.2.k	\(\chi_{1984}(497, \cdot)\)	n/a	120	2
1984.2.m	\(\chi_{1984}(495, \cdot)\)	n/a	124	2
1984.2.n	\(\chi_{1984}(1025, \cdot)\)	n/a	248	4
1984.2.o	\(\chi_{1984}(1215, \cdot)\)	n/a	124	2
1984.2.t	\(\chi_{1984}(1121, \cdot)\)	n/a	128	2
1984.2.u	\(\chi_{1984}(223, \cdot)\)	n/a	128	2
1984.2.v	\(\chi_{1984}(249, \cdot)\)	None	0	4
1984.2.w	\(\chi_{1984}(247, \cdot)\)	None	0	4
1984.2.bb	\(\chi_{1984}(511, \cdot)\)	n/a	248	4
1984.2.bc	\(\chi_{1984}(33, \cdot)\)	n/a	256	4
1984.2.bd	\(\chi_{1984}(1503, \cdot)\)	n/a	256	4
1984.2.bh	\(\chi_{1984}(367, \cdot)\)	n/a	248	4
1984.2.bj	\(\chi_{1984}(273, \cdot)\)	n/a	248	4
1984.2.bk	\(\chi_{1984}(193, \cdot)\)	n/a	496	8
1984.2.bl	\(\chi_{1984}(123, \cdot)\)	n/a	2032	8
1984.2.bo	\(\chi_{1984}(125, \cdot)\)	n/a	1920	8
1984.2.bp	\(\chi_{1984}(15, \cdot)\)	n/a	496	8
1984.2.br	\(\chi_{1984}(529, \cdot)\)	n/a	496	8
1984.2.bt	\(\chi_{1984}(119, \cdot)\)	None	0	8
1984.2.bu	\(\chi_{1984}(25, \cdot)\)	None	0	8
1984.2.bz	\(\chi_{1984}(415, \cdot)\)	n/a	512	8
1984.2.ca	\(\chi_{1984}(289, \cdot)\)	n/a	512	8
1984.2.cb	\(\chi_{1984}(127, \cdot)\)	n/a	496	8
1984.2.cg	\(\chi_{1984}(23, \cdot)\)	None	0	16
1984.2.ch	\(\chi_{1984}(233, \cdot)\)	None	0	16
1984.2.cj	\(\chi_{1984}(99, \cdot)\)	n/a	4064	16
1984.2.ck	\(\chi_{1984}(5, \cdot)\)	n/a	4064	16
1984.2.cm	\(\chi_{1984}(49, \cdot)\)	n/a	992	16
1984.2.co	\(\chi_{1984}(79, \cdot)\)	n/a	992	16
1984.2.cr	\(\chi_{1984}(27, \cdot)\)	n/a	8128	32
1984.2.cs	\(\chi_{1984}(101, \cdot)\)	n/a	8128	32
1984.2.cw	\(\chi_{1984}(9, \cdot)\)	None	0	32
1984.2.cx	\(\chi_{1984}(55, \cdot)\)	None	0	32
1984.2.cy	\(\chi_{1984}(3, \cdot)\)	n/a	16256	64
1984.2.db	\(\chi_{1984}(45, \cdot)\)	n/a	16256	64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1984))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1984)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(992))\)\(^{\oplus 2}\)