Space of modular forms of level 966 and weight 2

• Label: 966.2
• Level: 966
• Weight: 2
• Dimension: 6045
• Nonzero newspaces: 16
• Newform subspaces: 70
• Sturm bound: 101376
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 70 \)
Sturm bound:			\(101376\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(966))\).

	Total	New	Old
Modular forms	26400	6045	20355
Cusp forms	24289	6045	18244
Eisenstein series	2111	0	2111

Trace form

6045 * q - 3 * q^2 + q^3 + 5 * q^4 + 6 * q^5 + 9 * q^6 + 17 * q^7 - 3 * q^8 + 13 * q^9 + 6 * q^10 + 12 * q^11 + q^12 - 10 * q^13 - 15 * q^14 + 26 * q^15 - 3 * q^16 + 58 * q^17 + 61 * q^18 + 60 * q^19 + 70 * q^20 + 31 * q^21 + 52 * q^22 + 141 * q^23 - 15 * q^24 + 131 * q^25 + 70 * q^26 + 133 * q^27 + 53 * q^28 + 46 * q^29 + 94 * q^30 + 72 * q^31 - 3 * q^32 + 56 * q^33 - 6 * q^34 + 50 * q^35 + 13 * q^36 + 174 * q^37 + 12 * q^38 + 102 * q^39 + 6 * q^40 + 58 * q^41 + 45 * q^42 + 204 * q^43 + 12 * q^44 + 6 * q^45 + q^46 + 104 * q^47 + q^48 + 129 * q^49 + 3 * q^50 + 10 * q^51 - 58 * q^52 - 2 * q^53 - 83 * q^54 + 32 * q^55 + 9 * q^56 - 48 * q^57 - 114 * q^58 + 4 * q^59 - 86 * q^60 - 106 * q^61 - 48 * q^62 - 157 * q^63 + 5 * q^64 - 84 * q^65 - 212 * q^66 - 156 * q^67 - 30 * q^68 - 243 * q^69 - 90 * q^70 - 72 * q^71 - 67 * q^72 - 118 * q^73 - 42 * q^74 - 281 * q^75 - 28 * q^76 + 36 * q^77 - 126 * q^78 + 88 * q^79 + 6 * q^80 + 21 * q^81 + 18 * q^82 + 76 * q^83 + 15 * q^84 + 148 * q^85 - 12 * q^86 + 162 * q^87 - 12 * q^88 + 10 * q^89 + 6 * q^90 + 102 * q^91 - 23 * q^92 - 40 * q^93 + 120 * q^95 - 15 * q^96 + 258 * q^97 + 37 * q^98 + 184 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(966))\)

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
966.2.a	\(\chi_{966}(1, \cdot)\)	966.2.a.a	1	1
		966.2.a.b	1
		966.2.a.c	1
		966.2.a.d	1
		966.2.a.e	1
		966.2.a.f	1
		966.2.a.g	1
		966.2.a.h	1
		966.2.a.i	1
		966.2.a.j	1
		966.2.a.k	1
		966.2.a.l	2
		966.2.a.m	2
		966.2.a.n	2
		966.2.a.o	2
		966.2.a.p	2
966.2.f	\(\chi_{966}(461, \cdot)\)	966.2.f.a	4	1
		966.2.f.b	24
		966.2.f.c	28
966.2.g	\(\chi_{966}(643, \cdot)\)	966.2.g.a	4	1
		966.2.g.b	4
		966.2.g.c	4
		966.2.g.d	4
		966.2.g.e	16
966.2.h	\(\chi_{966}(827, \cdot)\)	966.2.h.a	24	1
		966.2.h.b	24
966.2.i	\(\chi_{966}(277, \cdot)\)	966.2.i.a	2	2
		966.2.i.b	2
		966.2.i.c	2
		966.2.i.d	2
		966.2.i.e	2
		966.2.i.f	2
		966.2.i.g	2
		966.2.i.h	4
		966.2.i.i	4
		966.2.i.j	4
		966.2.i.k	6
		966.2.i.l	8
		966.2.i.m	8
		966.2.i.n	8
966.2.j	\(\chi_{966}(137, \cdot)\)	966.2.j.a	128	2
966.2.k	\(\chi_{966}(229, \cdot)\)	966.2.k.a	32	2
		966.2.k.b	32
966.2.l	\(\chi_{966}(47, \cdot)\)	966.2.l.a	4	2
		966.2.l.b	4
		966.2.l.c	56
		966.2.l.d	56
966.2.q	\(\chi_{966}(85, \cdot)\)	966.2.q.a	10	10
		966.2.q.b	10
		966.2.q.c	10
		966.2.q.d	20
		966.2.q.e	20
		966.2.q.f	30
		966.2.q.g	30
		966.2.q.h	30
		966.2.q.i	40
		966.2.q.j	40
966.2.r	\(\chi_{966}(113, \cdot)\)	966.2.r.a	240	10
		966.2.r.b	240
966.2.s	\(\chi_{966}(97, \cdot)\)	966.2.s.a	160	10
		966.2.s.b	160
966.2.t	\(\chi_{966}(41, \cdot)\)	966.2.t.a	640	10
966.2.y	\(\chi_{966}(25, \cdot)\)	966.2.y.a	160	20
		966.2.y.b	160
		966.2.y.c	160
		966.2.y.d	160
966.2.bd	\(\chi_{966}(59, \cdot)\)	966.2.bd.a	1280	20
966.2.be	\(\chi_{966}(19, \cdot)\)	966.2.be.a	320	20
		966.2.be.b	320
966.2.bf	\(\chi_{966}(11, \cdot)\)	966.2.bf.a	1280	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(966))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(966)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 2}\)