Space of modular forms of level 968 and weight 2

• Label: 968.2
• Level: 968
• Weight: 2
• Dimension: 15785
• Nonzero newspaces: 12
• Newform subspaces: 80
• Sturm bound: 116160
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 80 \)
Sturm bound:			\(116160\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(968))\).

	Total	New	Old
Modular forms	30000	16347	13653
Cusp forms	28081	15785	12296
Eisenstein series	1919	562	1357

Trace form

15785 * q - 90 * q^2 - 90 * q^3 - 90 * q^4 - 90 * q^6 - 90 * q^7 - 90 * q^8 - 180 * q^9 - 90 * q^10 - 100 * q^11 - 170 * q^12 - 90 * q^14 - 70 * q^15 - 90 * q^16 - 160 * q^17 - 90 * q^18 - 60 * q^19 - 90 * q^20 + 40 * q^21 - 100 * q^22 - 150 * q^23 - 90 * q^24 - 140 * q^25 - 90 * q^26 - 60 * q^27 - 90 * q^28 + 20 * q^29 - 150 * q^30 - 70 * q^31 - 110 * q^32 - 215 * q^33 - 250 * q^34 - 150 * q^35 - 250 * q^36 - 190 * q^38 - 210 * q^39 - 230 * q^40 - 240 * q^41 - 310 * q^42 - 170 * q^43 - 170 * q^44 - 60 * q^45 - 230 * q^46 - 150 * q^47 - 310 * q^48 - 240 * q^49 - 230 * q^50 - 200 * q^51 - 190 * q^52 + 40 * q^53 - 250 * q^54 - 110 * q^55 - 250 * q^56 - 130 * q^57 - 110 * q^58 - 20 * q^59 - 190 * q^60 + 40 * q^61 - 90 * q^62 - 70 * q^63 - 90 * q^64 - 100 * q^65 - 100 * q^66 - 90 * q^67 - 90 * q^68 + 80 * q^69 + 50 * q^70 - 50 * q^71 + 10 * q^72 - 200 * q^73 + 10 * q^74 - 180 * q^75 + 70 * q^76 + 10 * q^77 + 70 * q^78 - 250 * q^79 + 130 * q^80 - 230 * q^81 + 110 * q^82 - 280 * q^83 + 150 * q^84 - 120 * q^85 + 30 * q^86 - 310 * q^87 + 60 * q^88 - 400 * q^89 + 190 * q^90 - 310 * q^91 + 70 * q^92 - 60 * q^93 + 150 * q^94 - 250 * q^95 + 50 * q^96 - 210 * q^97 + 130 * q^98 - 150 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)

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
968.2.a	\(\chi_{968}(1, \cdot)\)	968.2.a.a	1	1
		968.2.a.b	1
		968.2.a.c	1
		968.2.a.d	1
		968.2.a.e	1
		968.2.a.f	2
		968.2.a.g	2
		968.2.a.h	2
		968.2.a.i	2
		968.2.a.j	2
		968.2.a.k	2
		968.2.a.l	2
		968.2.a.m	4
		968.2.a.n	4
968.2.c	\(\chi_{968}(485, \cdot)\)	968.2.c.a	2	1
		968.2.c.b	4
		968.2.c.c	8
		968.2.c.d	10
		968.2.c.e	10
		968.2.c.f	10
		968.2.c.g	16
		968.2.c.h	20
		968.2.c.i	20
968.2.e	\(\chi_{968}(967, \cdot)\)	None	0	1
968.2.g	\(\chi_{968}(483, \cdot)\)	968.2.g.a	8	1
		968.2.g.b	8
		968.2.g.c	20
		968.2.g.d	32
		968.2.g.e	32
968.2.i	\(\chi_{968}(9, \cdot)\)	968.2.i.a	4	4
		968.2.i.b	4
		968.2.i.c	4
		968.2.i.d	4
		968.2.i.e	4
		968.2.i.f	4
		968.2.i.g	4
		968.2.i.h	4
		968.2.i.i	4
		968.2.i.j	4
		968.2.i.k	4
		968.2.i.l	4
		968.2.i.m	4
		968.2.i.n	8
		968.2.i.o	8
		968.2.i.p	8
		968.2.i.q	8
		968.2.i.r	8
		968.2.i.s	8
		968.2.i.t	8
968.2.k	\(\chi_{968}(403, \cdot)\)	968.2.k.a	8	4
		968.2.k.b	8
		968.2.k.c	8
		968.2.k.d	8
		968.2.k.e	32
		968.2.k.f	32
		968.2.k.g	32
		968.2.k.h	32
		968.2.k.i	32
		968.2.k.j	80
		968.2.k.k	128
968.2.m	\(\chi_{968}(215, \cdot)\)	None	0	4
968.2.o	\(\chi_{968}(245, \cdot)\)	968.2.o.a	8	4
		968.2.o.b	16
		968.2.o.c	32
		968.2.o.d	40
		968.2.o.e	40
		968.2.o.f	40
		968.2.o.g	40
		968.2.o.h	40
		968.2.o.i	40
		968.2.o.j	40
		968.2.o.k	64
968.2.q	\(\chi_{968}(89, \cdot)\)	968.2.q.a	160	10
		968.2.q.b	170
968.2.r	\(\chi_{968}(87, \cdot)\)	None	0	10
968.2.t	\(\chi_{968}(45, \cdot)\)	968.2.t.a	1300	10
968.2.w	\(\chi_{968}(43, \cdot)\)	968.2.w.a	20	10
		968.2.w.b	1280
968.2.y	\(\chi_{968}(25, \cdot)\)	968.2.y.a	640	40
		968.2.y.b	680
968.2.ba	\(\chi_{968}(19, \cdot)\)	968.2.ba.a	80	40
		968.2.ba.b	5120
968.2.bd	\(\chi_{968}(5, \cdot)\)	968.2.bd.a	5200	40
968.2.bf	\(\chi_{968}(7, \cdot)\)	None	0	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(968))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(968)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)