Space of modular forms of level 666 and weight 2

• Label: 666.2
• Level: 666
• Weight: 2
• Dimension: 3245
• Nonzero newspaces: 24
• Newform subspaces: 83
• Sturm bound: 49248
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 83 \)
Sturm bound:			\(49248\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(666))\).

	Total	New	Old
Modular forms	12888	3245	9643
Cusp forms	11737	3245	8492
Eisenstein series	1151	0	1151

Trace form

3245 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 - 6 * q^6 + 4 * q^7 - 4 * q^8 - 6 * q^9 - 6 * q^11 + 4 * q^13 + 4 * q^14 + 2 * q^16 + 12 * q^17 + 12 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 - 12 * q^23 + 6 * q^24 - 10 * q^25 + q^26 + 4 * q^28 + 48 * q^29 + 100 * q^31 + 2 * q^32 + 18 * q^33 + 66 * q^34 + 108 * q^35 - 6 * q^36 + 92 * q^37 + 34 * q^38 + 45 * q^40 + 126 * q^41 + 70 * q^43 + 12 * q^44 + 96 * q^46 + 24 * q^47 - 6 * q^48 + 42 * q^49 - q^50 - 18 * q^51 + 4 * q^52 - 48 * q^53 - 18 * q^54 + 4 * q^56 - 6 * q^57 + 12 * q^58 + 42 * q^59 + 61 * q^61 + 16 * q^62 + 24 * q^63 - 4 * q^64 + 81 * q^65 + 46 * q^67 - 6 * q^68 + 120 * q^71 - 6 * q^72 + 28 * q^73 - 4 * q^74 + 30 * q^75 - 2 * q^76 + 60 * q^77 + 12 * q^78 + 64 * q^79 + 18 * q^81 - 36 * q^82 + 60 * q^83 + 12 * q^84 + 81 * q^85 - 2 * q^86 - 36 * q^87 - 6 * q^88 + 21 * q^89 - 16 * q^91 - 120 * q^92 - 216 * q^93 - 228 * q^94 - 432 * q^95 - 422 * q^97 - 420 * q^98 - 396 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)

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
666.2.a	\(\chi_{666}(1, \cdot)\)	666.2.a.a	1	1
		666.2.a.b	1
		666.2.a.c	1
		666.2.a.d	1
		666.2.a.e	1
		666.2.a.f	1
		666.2.a.g	1
		666.2.a.h	2
		666.2.a.i	2
		666.2.a.j	2
		666.2.a.k	2
666.2.c	\(\chi_{666}(73, \cdot)\)	666.2.c.a	2	1
		666.2.c.b	4
		666.2.c.c	4
		666.2.c.d	4
666.2.e	\(\chi_{666}(223, \cdot)\)	666.2.e.a	2	2
		666.2.e.b	2
		666.2.e.c	12
		666.2.e.d	14
		666.2.e.e	20
		666.2.e.f	22
666.2.f	\(\chi_{666}(343, \cdot)\)	666.2.f.a	2	2
		666.2.f.b	2
		666.2.f.c	2
		666.2.f.d	2
		666.2.f.e	2
		666.2.f.f	2
		666.2.f.g	4
		666.2.f.h	4
		666.2.f.i	4
		666.2.f.j	6
666.2.g	\(\chi_{666}(211, \cdot)\)	666.2.g.a	2	2
		666.2.g.b	36
		666.2.g.c	38
666.2.h	\(\chi_{666}(121, \cdot)\)	666.2.h.a	2	2
		666.2.h.b	36
		666.2.h.c	38
666.2.j	\(\chi_{666}(179, \cdot)\)	666.2.j.a	4	2
		666.2.j.b	4
		666.2.j.c	4
		666.2.j.d	8
666.2.k	\(\chi_{666}(175, \cdot)\)	666.2.k.a	76	2
666.2.q	\(\chi_{666}(295, \cdot)\)	666.2.q.a	4	2
		666.2.q.b	72
666.2.s	\(\chi_{666}(307, \cdot)\)	666.2.s.a	4	2
		666.2.s.b	4
		666.2.s.c	4
		666.2.s.d	4
		666.2.s.e	4
		666.2.s.f	8
666.2.t	\(\chi_{666}(85, \cdot)\)	666.2.t.a	76	2
666.2.w	\(\chi_{666}(7, \cdot)\)	666.2.w.a	114	6
		666.2.w.b	114
666.2.x	\(\chi_{666}(127, \cdot)\)	666.2.x.a	6	6
		666.2.x.b	6
		666.2.x.c	6
		666.2.x.d	6
		666.2.x.e	6
		666.2.x.f	12
		666.2.x.g	12
		666.2.x.h	24
		666.2.x.i	24
666.2.y	\(\chi_{666}(229, \cdot)\)	666.2.y.a	114	6
		666.2.y.b	114
666.2.ba	\(\chi_{666}(23, \cdot)\)	666.2.ba.a	152	4
666.2.bb	\(\chi_{666}(191, \cdot)\)	666.2.bb.a	152	4
666.2.be	\(\chi_{666}(125, \cdot)\)	666.2.be.a	8	4
		666.2.be.b	8
		666.2.be.c	8
		666.2.be.d	16
666.2.bf	\(\chi_{666}(245, \cdot)\)	666.2.bf.a	152	4
666.2.bj	\(\chi_{666}(289, \cdot)\)	666.2.bj.a	12	6
		666.2.bj.b	12
		666.2.bj.c	12
		666.2.bj.d	12
		666.2.bj.e	24
		666.2.bj.f	24
666.2.bk	\(\chi_{666}(115, \cdot)\)	666.2.bk.a	228	6
666.2.bp	\(\chi_{666}(25, \cdot)\)	666.2.bp.a	228	6
666.2.br	\(\chi_{666}(59, \cdot)\)	666.2.br.a	456	12
666.2.bs	\(\chi_{666}(17, \cdot)\)	666.2.bs.a	72	12
		666.2.bs.b	96
666.2.bv	\(\chi_{666}(5, \cdot)\)	666.2.bv.a	456	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(666))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(666)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 2}\)