Space of modular forms of level 960 and weight 2

• Label: 960.2
• Level: 960
• Weight: 2
• Dimension: 9372
• Nonzero newspaces: 28
• Newform subspaces: 128
• Sturm bound: 98304
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Newform subspaces:			\( 128 \)
Sturm bound:			\(98304\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(960))\).

	Total	New	Old
Modular forms	25728	9636	16092
Cusp forms	23425	9372	14053
Eisenstein series	2303	264	2039

Trace form

9372 * q - 12 * q^3 - 32 * q^4 - 48 * q^6 - 32 * q^7 - 20 * q^9 - 48 * q^10 - 16 * q^11 - 16 * q^12 - 64 * q^13 - 24 * q^15 - 96 * q^16 - 32 * q^17 - 16 * q^18 - 56 * q^19 - 40 * q^21 + 64 * q^24 - 28 * q^25 + 160 * q^26 + 12 * q^27 + 128 * q^28 + 64 * q^29 + 56 * q^30 + 16 * q^31 + 160 * q^32 + 64 * q^33 + 128 * q^34 + 24 * q^35 + 112 * q^36 + 32 * q^37 + 160 * q^38 + 40 * q^39 + 32 * q^40 + 64 * q^41 + 64 * q^42 - 8 * q^43 + 32 * q^44 + 20 * q^45 - 96 * q^46 - 16 * q^48 - 28 * q^49 - 48 * q^50 + 96 * q^51 - 224 * q^52 - 48 * q^54 + 120 * q^55 - 224 * q^56 + 56 * q^57 - 320 * q^58 + 320 * q^59 - 120 * q^60 - 96 * q^61 - 192 * q^62 + 112 * q^63 - 416 * q^64 + 80 * q^65 - 208 * q^66 + 424 * q^67 - 192 * q^68 + 8 * q^69 - 240 * q^70 + 384 * q^71 - 16 * q^72 + 88 * q^73 - 224 * q^74 + 152 * q^75 - 352 * q^76 + 96 * q^77 - 160 * q^78 + 208 * q^79 - 48 * q^80 - 84 * q^81 - 32 * q^82 + 80 * q^83 - 240 * q^84 + 96 * q^85 - 16 * q^87 - 32 * q^88 + 64 * q^89 - 168 * q^90 - 64 * q^91 - 32 * q^93 - 32 * q^94 + 48 * q^95 - 320 * q^96 - 56 * q^97 - 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)

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
960.2.a	\(\chi_{960}(1, \cdot)\)	960.2.a.a	1	1
		960.2.a.b	1
		960.2.a.c	1
		960.2.a.d	1
		960.2.a.e	1
		960.2.a.f	1
		960.2.a.g	1
		960.2.a.h	1
		960.2.a.i	1
		960.2.a.j	1
		960.2.a.k	1
		960.2.a.l	1
		960.2.a.m	1
		960.2.a.n	1
		960.2.a.o	1
		960.2.a.p	1
960.2.b	\(\chi_{960}(671, \cdot)\)	960.2.b.a	4	1
		960.2.b.b	4
		960.2.b.c	12
		960.2.b.d	12
960.2.d	\(\chi_{960}(289, \cdot)\)	960.2.d.a	2	1
		960.2.d.b	2
		960.2.d.c	2
		960.2.d.d	2
		960.2.d.e	8
		960.2.d.f	8
960.2.f	\(\chi_{960}(769, \cdot)\)	960.2.f.a	2	1
		960.2.f.b	2
		960.2.f.c	2
		960.2.f.d	2
		960.2.f.e	2
		960.2.f.f	2
		960.2.f.g	2
		960.2.f.h	2
		960.2.f.i	2
		960.2.f.j	2
		960.2.f.k	4
960.2.h	\(\chi_{960}(191, \cdot)\)	960.2.h.a	4	1
		960.2.h.b	4
		960.2.h.c	4
		960.2.h.d	4
		960.2.h.e	4
		960.2.h.f	4
		960.2.h.g	8
960.2.k	\(\chi_{960}(481, \cdot)\)	960.2.k.a	2	1
		960.2.k.b	2
		960.2.k.c	2
		960.2.k.d	2
		960.2.k.e	4
		960.2.k.f	4
960.2.m	\(\chi_{960}(479, \cdot)\)	960.2.m.a	8	1
		960.2.m.b	8
		960.2.m.c	16
		960.2.m.d	16
960.2.o	\(\chi_{960}(959, \cdot)\)	960.2.o.a	4	1
		960.2.o.b	4
		960.2.o.c	4
		960.2.o.d	8
		960.2.o.e	24
960.2.s	\(\chi_{960}(241, \cdot)\)	960.2.s.a	4	2
		960.2.s.b	8
		960.2.s.c	20
960.2.t	\(\chi_{960}(239, \cdot)\)	960.2.t.a	8	2
		960.2.t.b	80
960.2.v	\(\chi_{960}(257, \cdot)\)	960.2.v.a	4	2
		960.2.v.b	4
		960.2.v.c	4
		960.2.v.d	4
		960.2.v.e	4
		960.2.v.f	4
		960.2.v.g	4
		960.2.v.h	4
		960.2.v.i	4
		960.2.v.j	4
		960.2.v.k	4
		960.2.v.l	4
		960.2.v.m	16
		960.2.v.n	24
960.2.w	\(\chi_{960}(127, \cdot)\)	960.2.w.a	4	2
		960.2.w.b	4
		960.2.w.c	4
		960.2.w.d	8
		960.2.w.e	8
		960.2.w.f	8
		960.2.w.g	12
960.2.y	\(\chi_{960}(847, \cdot)\)	960.2.y.a	2	2
		960.2.y.b	2
		960.2.y.c	2
		960.2.y.d	6
		960.2.y.e	16
		960.2.y.f	20
960.2.bb	\(\chi_{960}(497, \cdot)\)	960.2.bb.a	88	2
960.2.bc	\(\chi_{960}(367, \cdot)\)	960.2.bc.a	2	2
		960.2.bc.b	2
		960.2.bc.c	2
		960.2.bc.d	6
		960.2.bc.e	16
		960.2.bc.f	20
960.2.bf	\(\chi_{960}(17, \cdot)\)	960.2.bf.a	88	2
960.2.bh	\(\chi_{960}(223, \cdot)\)	960.2.bh.a	4	2
		960.2.bh.b	4
		960.2.bh.c	4
		960.2.bh.d	4
		960.2.bh.e	8
		960.2.bh.f	8
		960.2.bh.g	8
		960.2.bh.h	8
960.2.bi	\(\chi_{960}(353, \cdot)\)	960.2.bi.a	4	2
		960.2.bi.b	4
		960.2.bi.c	4
		960.2.bi.d	4
		960.2.bi.e	8
		960.2.bi.f	8
		960.2.bi.g	32
		960.2.bi.h	32
960.2.bk	\(\chi_{960}(431, \cdot)\)	960.2.bk.a	4	2
		960.2.bk.b	60
960.2.bl	\(\chi_{960}(49, \cdot)\)	960.2.bl.a	48	2
960.2.bo	\(\chi_{960}(103, \cdot)\)	None	0	4
960.2.br	\(\chi_{960}(233, \cdot)\)	None	0	4
960.2.bs	\(\chi_{960}(119, \cdot)\)	None	0	4
960.2.bv	\(\chi_{960}(121, \cdot)\)	None	0	4
960.2.bx	\(\chi_{960}(71, \cdot)\)	None	0	4
960.2.by	\(\chi_{960}(169, \cdot)\)	None	0	4
960.2.cb	\(\chi_{960}(137, \cdot)\)	None	0	4
960.2.cc	\(\chi_{960}(7, \cdot)\)	None	0	4
960.2.cf	\(\chi_{960}(173, \cdot)\)	960.2.cf.a	1504	8
960.2.cg	\(\chi_{960}(43, \cdot)\)	960.2.cg.a	768	8
960.2.ci	\(\chi_{960}(61, \cdot)\)	960.2.ci.a	240	8
		960.2.ci.b	272
960.2.ck	\(\chi_{960}(109, \cdot)\)	960.2.ck.a	768	8
960.2.cn	\(\chi_{960}(11, \cdot)\)	960.2.cn.a	1024	8
960.2.cp	\(\chi_{960}(59, \cdot)\)	960.2.cp.a	32	8
		960.2.cp.b	1472
960.2.cr	\(\chi_{960}(53, \cdot)\)	960.2.cr.a	1504	8
960.2.cs	\(\chi_{960}(163, \cdot)\)	960.2.cs.a	768	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(960))\) into lower level spaces

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