Space of modular forms of level 1920 and weight 2

• Label: 1920.2
• Level: 1920
• Weight: 2
• Dimension: 37728
• Nonzero newspaces: 36
• Sturm bound: 393216
• Trace bound: 81

Defining parameters

Level:	\( N \)	=	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(393216\)
Trace bound:			\(81\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1920))\).

	Total	New	Old
Modular forms	100864	38304	62560
Cusp forms	95745	37728	58017
Eisenstein series	5119	576	4543

Trace form

37728 * q - 24 * q^3 - 64 * q^4 - 96 * q^6 - 48 * q^7 - 40 * q^9 - 96 * q^10 - 32 * q^12 - 64 * q^13 - 40 * q^15 - 192 * q^16 - 32 * q^18 - 48 * q^19 - 120 * q^21 - 64 * q^22 - 32 * q^23 - 32 * q^24 - 152 * q^25 - 72 * q^27 - 64 * q^28 - 64 * q^29 - 48 * q^30 - 224 * q^31 - 128 * q^33 - 64 * q^34 - 48 * q^35 - 96 * q^36 - 128 * q^37 - 72 * q^39 - 96 * q^40 - 64 * q^41 - 32 * q^42 - 80 * q^43 - 68 * q^45 - 192 * q^46 - 32 * q^48 + 16 * q^49 + 96 * q^50 - 64 * q^51 + 320 * q^52 + 128 * q^53 + 32 * q^54 - 8 * q^55 + 448 * q^56 + 88 * q^57 + 512 * q^58 + 128 * q^59 + 144 * q^60 + 64 * q^61 + 384 * q^62 + 48 * q^63 + 704 * q^64 + 128 * q^65 + 288 * q^66 + 112 * q^67 + 384 * q^68 + 120 * q^69 + 288 * q^70 + 128 * q^71 - 32 * q^72 + 176 * q^73 + 448 * q^74 - 4 * q^75 + 320 * q^76 + 128 * q^77 + 160 * q^78 + 32 * q^79 + 96 * q^80 - 80 * q^81 - 64 * q^82 - 32 * q^84 - 16 * q^85 + 88 * q^87 - 64 * q^88 - 48 * q^90 - 144 * q^91 + 64 * q^93 - 64 * q^94 - 96 * q^96 - 128 * q^97 + 104 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1920))\)

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
1920.2.a	\(\chi_{1920}(1, \cdot)\)	1920.2.a.a	1	1
		1920.2.a.b	1
		1920.2.a.c	1
		1920.2.a.d	1
		1920.2.a.e	1
		1920.2.a.f	1
		1920.2.a.g	1
		1920.2.a.h	1
		1920.2.a.i	1
		1920.2.a.j	1
		1920.2.a.k	1
		1920.2.a.l	1
		1920.2.a.m	1
		1920.2.a.n	1
		1920.2.a.o	1
		1920.2.a.p	1
		1920.2.a.q	1
		1920.2.a.r	1
		1920.2.a.s	1
		1920.2.a.t	1
		1920.2.a.u	1
		1920.2.a.v	1
		1920.2.a.w	1
		1920.2.a.x	1
		1920.2.a.y	2
		1920.2.a.z	2
		1920.2.a.ba	2
		1920.2.a.bb	2
1920.2.b	\(\chi_{1920}(191, \cdot)\)	1920.2.b.a	8	1
		1920.2.b.b	8
		1920.2.b.c	8
		1920.2.b.d	8
		1920.2.b.e	8
		1920.2.b.f	8
		1920.2.b.g	8
		1920.2.b.h	8
1920.2.d	\(\chi_{1920}(1729, \cdot)\)	1920.2.d.a	4	1
		1920.2.d.b	4
		1920.2.d.c	6
		1920.2.d.d	6
		1920.2.d.e	6
		1920.2.d.f	6
		1920.2.d.g	8
		1920.2.d.h	8
1920.2.f	\(\chi_{1920}(769, \cdot)\)	1920.2.f.a	2	1
		1920.2.f.b	2
		1920.2.f.c	2
		1920.2.f.d	2
		1920.2.f.e	2
		1920.2.f.f	2
		1920.2.f.g	2
		1920.2.f.h	2
		1920.2.f.i	2
		1920.2.f.j	2
		1920.2.f.k	2
		1920.2.f.l	2
		1920.2.f.m	6
		1920.2.f.n	6
		1920.2.f.o	6
		1920.2.f.p	6
1920.2.h	\(\chi_{1920}(1151, \cdot)\)	1920.2.h.a	4	1
		1920.2.h.b	4
		1920.2.h.c	4
		1920.2.h.d	4
		1920.2.h.e	4
		1920.2.h.f	4
		1920.2.h.g	4
		1920.2.h.h	4
		1920.2.h.i	4
		1920.2.h.j	4
		1920.2.h.k	4
		1920.2.h.l	4
		1920.2.h.m	4
		1920.2.h.n	4
		1920.2.h.o	4
		1920.2.h.p	4
1920.2.k	\(\chi_{1920}(961, \cdot)\)	1920.2.k.a	2	1
		1920.2.k.b	2
		1920.2.k.c	2
		1920.2.k.d	2
		1920.2.k.e	2
		1920.2.k.f	2
		1920.2.k.g	2
		1920.2.k.h	2
		1920.2.k.i	4
		1920.2.k.j	4
		1920.2.k.k	4
		1920.2.k.l	4
1920.2.m	\(\chi_{1920}(959, \cdot)\)	1920.2.m.a	4	1
		1920.2.m.b	4
		1920.2.m.c	4
		1920.2.m.d	4
		1920.2.m.e	4
		1920.2.m.f	4
		1920.2.m.g	4
		1920.2.m.h	4
		1920.2.m.i	4
		1920.2.m.j	4
		1920.2.m.k	4
		1920.2.m.l	4
		1920.2.m.m	4
		1920.2.m.n	4
		1920.2.m.o	4
		1920.2.m.p	4
		1920.2.m.q	4
		1920.2.m.r	4
		1920.2.m.s	4
		1920.2.m.t	4
		1920.2.m.u	4
		1920.2.m.v	4
		1920.2.m.w	8
1920.2.o	\(\chi_{1920}(1919, \cdot)\)	1920.2.o.a	24	1
		1920.2.o.b	24
		1920.2.o.c	24
		1920.2.o.d	24
1920.2.s	\(\chi_{1920}(481, \cdot)\)	1920.2.s.a	4	2
		1920.2.s.b	4
		1920.2.s.c	8
		1920.2.s.d	8
		1920.2.s.e	20
		1920.2.s.f	20
1920.2.t	\(\chi_{1920}(479, \cdot)\)	n/a	176	2
1920.2.v	\(\chi_{1920}(257, \cdot)\)	n/a	192	2
1920.2.w	\(\chi_{1920}(127, \cdot)\)	1920.2.w.a	4	2
		1920.2.w.b	4
		1920.2.w.c	4
		1920.2.w.d	4
		1920.2.w.e	8
		1920.2.w.f	8
		1920.2.w.g	8
		1920.2.w.h	8
		1920.2.w.i	12
		1920.2.w.j	12
		1920.2.w.k	12
		1920.2.w.l	12
1920.2.y	\(\chi_{1920}(223, \cdot)\)	1920.2.y.a	2	2
		1920.2.y.b	2
		1920.2.y.c	2
		1920.2.y.d	2
		1920.2.y.e	2
		1920.2.y.f	2
		1920.2.y.g	6
		1920.2.y.h	6
		1920.2.y.i	16
		1920.2.y.j	16
		1920.2.y.k	20
		1920.2.y.l	20
1920.2.bb	\(\chi_{1920}(737, \cdot)\)	n/a	176	2
1920.2.bc	\(\chi_{1920}(607, \cdot)\)	1920.2.bc.a	2	2
		1920.2.bc.b	2
		1920.2.bc.c	2
		1920.2.bc.d	2
		1920.2.bc.e	2
		1920.2.bc.f	2
		1920.2.bc.g	6
		1920.2.bc.h	6
		1920.2.bc.i	16
		1920.2.bc.j	16
		1920.2.bc.k	20
		1920.2.bc.l	20
1920.2.bf	\(\chi_{1920}(353, \cdot)\)	n/a	176	2
1920.2.bh	\(\chi_{1920}(703, \cdot)\)	1920.2.bh.a	4	2
		1920.2.bh.b	4
		1920.2.bh.c	4
		1920.2.bh.d	4
		1920.2.bh.e	4
		1920.2.bh.f	4
		1920.2.bh.g	4
		1920.2.bh.h	4
		1920.2.bh.i	8
		1920.2.bh.j	8
		1920.2.bh.k	12
		1920.2.bh.l	12
		1920.2.bh.m	12
		1920.2.bh.n	12
1920.2.bi	\(\chi_{1920}(833, \cdot)\)	n/a	192	2
1920.2.bk	\(\chi_{1920}(671, \cdot)\)	n/a	128	2
1920.2.bl	\(\chi_{1920}(289, \cdot)\)	1920.2.bl.a	48	2
		1920.2.bl.b	48
1920.2.bo	\(\chi_{1920}(367, \cdot)\)	n/a	192	4
1920.2.br	\(\chi_{1920}(497, \cdot)\)	n/a	368	4
1920.2.bs	\(\chi_{1920}(239, \cdot)\)	n/a	368	4
1920.2.bv	\(\chi_{1920}(241, \cdot)\)	n/a	128	4
1920.2.bx	\(\chi_{1920}(431, \cdot)\)	n/a	256	4
1920.2.by	\(\chi_{1920}(49, \cdot)\)	n/a	192	4
1920.2.cb	\(\chi_{1920}(17, \cdot)\)	n/a	368	4
1920.2.cc	\(\chi_{1920}(847, \cdot)\)	n/a	192	4
1920.2.cf	\(\chi_{1920}(233, \cdot)\)	None	0	8
1920.2.cg	\(\chi_{1920}(103, \cdot)\)	None	0	8
1920.2.ci	\(\chi_{1920}(121, \cdot)\)	None	0	8
1920.2.ck	\(\chi_{1920}(169, \cdot)\)	None	0	8
1920.2.cn	\(\chi_{1920}(71, \cdot)\)	None	0	8
1920.2.cp	\(\chi_{1920}(119, \cdot)\)	None	0	8
1920.2.cr	\(\chi_{1920}(137, \cdot)\)	None	0	8
1920.2.cs	\(\chi_{1920}(7, \cdot)\)	None	0	8
1920.2.cw	\(\chi_{1920}(173, \cdot)\)	n/a	6080	16
1920.2.cx	\(\chi_{1920}(163, \cdot)\)	n/a	3072	16
1920.2.cy	\(\chi_{1920}(11, \cdot)\)	n/a	4096	16
1920.2.cz	\(\chi_{1920}(109, \cdot)\)	n/a	3072	16
1920.2.dc	\(\chi_{1920}(61, \cdot)\)	n/a	2048	16
1920.2.dd	\(\chi_{1920}(59, \cdot)\)	n/a	6080	16
1920.2.di	\(\chi_{1920}(43, \cdot)\)	n/a	3072	16
1920.2.dj	\(\chi_{1920}(53, \cdot)\)	n/a	6080	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 2}\)