Space of modular forms of level 3920 and weight 2

• Label: 3920.2
• Level: 3920
• Weight: 2
• Dimension: 222134
• Nonzero newspaces: 56
• Sturm bound: 1806336
• Trace bound: 14

Defining parameters

Level:	\( N \)	=	\( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(1806336\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3920))\).

	Total	New	Old
Modular forms	458304	224752	233552
Cusp forms	444865	222134	222731
Eisenstein series	13439	2618	10821

Trace form

222134 * q - 124 * q^2 - 92 * q^3 - 128 * q^4 - 233 * q^5 - 384 * q^6 - 108 * q^7 - 232 * q^8 - 34 * q^9 - 188 * q^10 - 286 * q^11 - 120 * q^12 - 172 * q^13 - 144 * q^14 - 265 * q^15 - 360 * q^16 - 288 * q^17 - 132 * q^18 - 142 * q^19 - 192 * q^20 - 564 * q^21 - 224 * q^22 - 180 * q^23 - 128 * q^24 - 103 * q^25 - 384 * q^26 - 170 * q^27 - 144 * q^28 - 338 * q^29 - 152 * q^30 - 338 * q^31 - 104 * q^32 - 350 * q^33 - 72 * q^34 - 180 * q^35 - 592 * q^36 - 180 * q^37 - 48 * q^38 - 58 * q^39 - 100 * q^40 - 74 * q^41 - 148 * q^43 + 128 * q^44 - 129 * q^45 - 96 * q^46 - 56 * q^47 + 400 * q^48 - 228 * q^49 - 480 * q^50 - 186 * q^51 + 344 * q^52 + 36 * q^53 + 592 * q^54 - 77 * q^55 - 264 * q^56 + 290 * q^57 + 232 * q^58 - 22 * q^59 + 116 * q^60 - 258 * q^61 + 272 * q^62 - 48 * q^63 + 88 * q^64 - 389 * q^65 + 32 * q^66 + 8 * q^67 + 56 * q^68 - 30 * q^69 - 168 * q^70 - 562 * q^71 + 128 * q^72 - 148 * q^73 - 216 * q^74 - 137 * q^75 - 464 * q^76 - 276 * q^77 - 352 * q^78 - 170 * q^79 - 276 * q^80 - 1096 * q^81 - 192 * q^82 - 208 * q^83 - 144 * q^84 - 511 * q^85 - 440 * q^86 - 154 * q^87 - 232 * q^88 - 246 * q^89 - 448 * q^90 - 198 * q^91 - 264 * q^92 - 350 * q^93 - 440 * q^94 - 11 * q^95 - 888 * q^96 - 374 * q^97 - 312 * q^98 + 240 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3920))\)

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
3920.2.a	\(\chi_{3920}(1, \cdot)\)	3920.2.a.a	1	1
		3920.2.a.b	1
		3920.2.a.c	1
		3920.2.a.d	1
		3920.2.a.e	1
		3920.2.a.f	1
		3920.2.a.g	1
		3920.2.a.h	1
		3920.2.a.i	1
		3920.2.a.j	1
		3920.2.a.k	1
		3920.2.a.l	1
		3920.2.a.m	1
		3920.2.a.n	1
		3920.2.a.o	1
		3920.2.a.p	1
		3920.2.a.q	1
		3920.2.a.r	1
		3920.2.a.s	1
		3920.2.a.t	1
		3920.2.a.u	1
		3920.2.a.v	1
		3920.2.a.w	1
		3920.2.a.x	1
		3920.2.a.y	1
		3920.2.a.z	1
		3920.2.a.ba	1
		3920.2.a.bb	1
		3920.2.a.bc	1
		3920.2.a.bd	1
		3920.2.a.be	1
		3920.2.a.bf	1
		3920.2.a.bg	1
		3920.2.a.bh	1
		3920.2.a.bi	1
		3920.2.a.bj	1
		3920.2.a.bk	1
		3920.2.a.bl	1
		3920.2.a.bm	2
		3920.2.a.bn	2
		3920.2.a.bo	2
		3920.2.a.bp	2
		3920.2.a.bq	2
		3920.2.a.br	2
		3920.2.a.bs	2
		3920.2.a.bt	2
		3920.2.a.bu	2
		3920.2.a.bv	2
		3920.2.a.bw	2
		3920.2.a.bx	2
		3920.2.a.by	2
		3920.2.a.bz	2
		3920.2.a.ca	2
		3920.2.a.cb	3
		3920.2.a.cc	3
		3920.2.a.cd	4
		3920.2.a.ce	4
3920.2.b	\(\chi_{3920}(1961, \cdot)\)	None	0	1
3920.2.e	\(\chi_{3920}(3919, \cdot)\)	n/a	120	1
3920.2.g	\(\chi_{3920}(1569, \cdot)\)	n/a	118	1
3920.2.h	\(\chi_{3920}(391, \cdot)\)	None	0	1
3920.2.k	\(\chi_{3920}(2351, \cdot)\)	3920.2.k.a	8	1
		3920.2.k.b	8
		3920.2.k.c	8
		3920.2.k.d	12
		3920.2.k.e	12
		3920.2.k.f	32
3920.2.l	\(\chi_{3920}(3529, \cdot)\)	None	0	1
3920.2.n	\(\chi_{3920}(1959, \cdot)\)	None	0	1
3920.2.q	\(\chi_{3920}(961, \cdot)\)	n/a	160	2
3920.2.r	\(\chi_{3920}(293, \cdot)\)	n/a	944	2
3920.2.t	\(\chi_{3920}(1667, \cdot)\)	n/a	964	2
3920.2.w	\(\chi_{3920}(1273, \cdot)\)	None	0	2
3920.2.x	\(\chi_{3920}(687, \cdot)\)	n/a	246	2
3920.2.bb	\(\chi_{3920}(589, \cdot)\)	n/a	964	2
3920.2.bc	\(\chi_{3920}(1371, \cdot)\)	n/a	640	2
3920.2.bd	\(\chi_{3920}(981, \cdot)\)	n/a	656	2
3920.2.be	\(\chi_{3920}(979, \cdot)\)	n/a	944	2
3920.2.bi	\(\chi_{3920}(1863, \cdot)\)	None	0	2
3920.2.bj	\(\chi_{3920}(97, \cdot)\)	n/a	232	2
3920.2.bl	\(\chi_{3920}(883, \cdot)\)	n/a	964	2
3920.2.bn	\(\chi_{3920}(1077, \cdot)\)	n/a	944	2
3920.2.bq	\(\chi_{3920}(999, \cdot)\)	None	0	2
3920.2.bs	\(\chi_{3920}(31, \cdot)\)	n/a	160	2
3920.2.bv	\(\chi_{3920}(569, \cdot)\)	None	0	2
3920.2.bw	\(\chi_{3920}(2529, \cdot)\)	n/a	232	2
3920.2.bz	\(\chi_{3920}(1991, \cdot)\)	None	0	2
3920.2.cb	\(\chi_{3920}(361, \cdot)\)	None	0	2
3920.2.cc	\(\chi_{3920}(1599, \cdot)\)	n/a	240	2
3920.2.ce	\(\chi_{3920}(561, \cdot)\)	n/a	672	6
3920.2.cg	\(\chi_{3920}(667, \cdot)\)	n/a	1888	4
3920.2.ci	\(\chi_{3920}(117, \cdot)\)	n/a	1888	4
3920.2.cj	\(\chi_{3920}(913, \cdot)\)	n/a	464	4
3920.2.cm	\(\chi_{3920}(263, \cdot)\)	None	0	4
3920.2.cp	\(\chi_{3920}(19, \cdot)\)	n/a	1888	4
3920.2.cq	\(\chi_{3920}(1341, \cdot)\)	n/a	1280	4
3920.2.cr	\(\chi_{3920}(411, \cdot)\)	n/a	1280	4
3920.2.cs	\(\chi_{3920}(949, \cdot)\)	n/a	1888	4
3920.2.cv	\(\chi_{3920}(863, \cdot)\)	n/a	480	4
3920.2.cy	\(\chi_{3920}(313, \cdot)\)	None	0	4
3920.2.da	\(\chi_{3920}(717, \cdot)\)	n/a	1888	4
3920.2.dc	\(\chi_{3920}(67, \cdot)\)	n/a	1888	4
3920.2.de	\(\chi_{3920}(279, \cdot)\)	None	0	6
3920.2.dg	\(\chi_{3920}(169, \cdot)\)	None	0	6
3920.2.dj	\(\chi_{3920}(111, \cdot)\)	n/a	672	6
3920.2.dk	\(\chi_{3920}(951, \cdot)\)	None	0	6
3920.2.dn	\(\chi_{3920}(449, \cdot)\)	n/a	996	6
3920.2.dp	\(\chi_{3920}(559, \cdot)\)	n/a	1008	6
3920.2.dq	\(\chi_{3920}(281, \cdot)\)	None	0	6
3920.2.ds	\(\chi_{3920}(81, \cdot)\)	n/a	1344	12
3920.2.dt	\(\chi_{3920}(13, \cdot)\)	n/a	8016	12
3920.2.dv	\(\chi_{3920}(267, \cdot)\)	n/a	8016	12
3920.2.dx	\(\chi_{3920}(183, \cdot)\)	None	0	12
3920.2.ea	\(\chi_{3920}(433, \cdot)\)	n/a	1992	12
3920.2.ed	\(\chi_{3920}(139, \cdot)\)	n/a	8016	12
3920.2.ee	\(\chi_{3920}(141, \cdot)\)	n/a	5376	12
3920.2.ef	\(\chi_{3920}(251, \cdot)\)	n/a	5376	12
3920.2.eg	\(\chi_{3920}(29, \cdot)\)	n/a	8016	12
3920.2.ej	\(\chi_{3920}(153, \cdot)\)	None	0	12
3920.2.em	\(\chi_{3920}(127, \cdot)\)	n/a	2016	12
3920.2.en	\(\chi_{3920}(43, \cdot)\)	n/a	8016	12
3920.2.ep	\(\chi_{3920}(237, \cdot)\)	n/a	8016	12
3920.2.er	\(\chi_{3920}(159, \cdot)\)	n/a	2016	12
3920.2.eu	\(\chi_{3920}(121, \cdot)\)	None	0	12
3920.2.ew	\(\chi_{3920}(311, \cdot)\)	None	0	12
3920.2.ex	\(\chi_{3920}(289, \cdot)\)	n/a	1992	12
3920.2.fa	\(\chi_{3920}(9, \cdot)\)	None	0	12
3920.2.fb	\(\chi_{3920}(271, \cdot)\)	n/a	1344	12
3920.2.ff	\(\chi_{3920}(199, \cdot)\)	None	0	12
3920.2.fh	\(\chi_{3920}(123, \cdot)\)	n/a	16032	24
3920.2.fj	\(\chi_{3920}(157, \cdot)\)	n/a	16032	24
3920.2.fl	\(\chi_{3920}(207, \cdot)\)	n/a	4032	24
3920.2.fm	\(\chi_{3920}(73, \cdot)\)	None	0	24
3920.2.fq	\(\chi_{3920}(109, \cdot)\)	n/a	16032	24
3920.2.fr	\(\chi_{3920}(131, \cdot)\)	n/a	10752	24
3920.2.fs	\(\chi_{3920}(221, \cdot)\)	n/a	10752	24
3920.2.ft	\(\chi_{3920}(59, \cdot)\)	n/a	16032	24
3920.2.fx	\(\chi_{3920}(17, \cdot)\)	n/a	3984	24
3920.2.fy	\(\chi_{3920}(23, \cdot)\)	None	0	24
3920.2.gb	\(\chi_{3920}(173, \cdot)\)	n/a	16032	24
3920.2.gd	\(\chi_{3920}(107, \cdot)\)	n/a	16032	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3920))\)\(^{\oplus 1}\)