Space of modular forms of level 888 and weight 2

• Label: 888.2
• Level: 888
• Weight: 2
• Dimension: 9080
• Nonzero newspaces: 27
• Newform subspaces: 70
• Sturm bound: 87552
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 27 \)
Newform subspaces:			\( 70 \)
Sturm bound:			\(87552\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(888))\).

	Total	New	Old
Modular forms	22752	9360	13392
Cusp forms	21025	9080	11945
Eisenstein series	1727	280	1447

Trace form

9080 * q + 4 * q^2 - 30 * q^3 - 64 * q^4 + 4 * q^5 - 40 * q^6 - 64 * q^7 - 8 * q^8 - 66 * q^9 - 80 * q^10 - 8 * q^11 - 52 * q^12 + 4 * q^13 - 8 * q^14 - 48 * q^15 - 72 * q^16 + 4 * q^17 - 24 * q^18 - 72 * q^19 + 16 * q^20 - 56 * q^22 - 12 * q^24 - 126 * q^25 + 16 * q^26 - 54 * q^27 - 72 * q^28 - 12 * q^29 - 28 * q^30 - 96 * q^31 - 16 * q^32 - 80 * q^33 - 112 * q^34 - 44 * q^36 - 6 * q^37 - 16 * q^38 - 24 * q^39 - 88 * q^40 + 4 * q^41 - 44 * q^42 - 40 * q^43 + 4 * q^45 - 56 * q^46 + 48 * q^47 - 20 * q^48 - 146 * q^49 + 4 * q^50 - 104 * q^52 + 4 * q^53 - 48 * q^54 - 56 * q^55 + 16 * q^56 - 88 * q^57 - 48 * q^58 + 64 * q^59 - 36 * q^60 + 94 * q^61 + 8 * q^62 + 64 * q^63 - 40 * q^64 + 122 * q^65 - 52 * q^66 - 48 * q^67 + 128 * q^69 - 56 * q^70 + 80 * q^71 - 60 * q^72 - 4 * q^73 - 16 * q^74 + 86 * q^75 - 24 * q^76 + 144 * q^77 - 52 * q^78 + 48 * q^79 + 94 * q^81 + 80 * q^83 - 20 * q^84 + 170 * q^85 + 16 * q^86 + 108 * q^87 - 104 * q^88 + 142 * q^89 - 28 * q^90 + 16 * q^93 - 120 * q^94 + 16 * q^95 - 84 * q^96 - 100 * q^97 - 12 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)

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
888.2.a	\(\chi_{888}(1, \cdot)\)	888.2.a.a	1	1
		888.2.a.b	1
		888.2.a.c	1
		888.2.a.d	1
		888.2.a.e	2
		888.2.a.f	2
		888.2.a.g	2
		888.2.a.h	2
		888.2.a.i	3
		888.2.a.j	3
888.2.c	\(\chi_{888}(443, \cdot)\)	888.2.c.a	16	1
		888.2.c.b	16
		888.2.c.c	20
		888.2.c.d	96
888.2.e	\(\chi_{888}(815, \cdot)\)	None	0	1
888.2.f	\(\chi_{888}(445, \cdot)\)	888.2.f.a	28	1
		888.2.f.b	44
888.2.h	\(\chi_{888}(73, \cdot)\)	888.2.h.a	2	1
		888.2.h.b	6
		888.2.h.c	10
888.2.j	\(\chi_{888}(371, \cdot)\)	888.2.j.a	4	1
		888.2.j.b	4
		888.2.j.c	136
888.2.l	\(\chi_{888}(887, \cdot)\)	None	0	1
888.2.o	\(\chi_{888}(517, \cdot)\)	888.2.o.a	76	1
888.2.q	\(\chi_{888}(121, \cdot)\)	888.2.q.a	2	2
		888.2.q.b	2
		888.2.q.c	2
		888.2.q.d	2
		888.2.q.e	6
		888.2.q.f	6
		888.2.q.g	6
		888.2.q.h	6
		888.2.q.i	8
888.2.r	\(\chi_{888}(43, \cdot)\)	888.2.r.a	2	2
		888.2.r.b	2
		888.2.r.c	2
		888.2.r.d	2
		888.2.r.e	72
		888.2.r.f	72
888.2.t	\(\chi_{888}(31, \cdot)\)	None	0	2
888.2.w	\(\chi_{888}(413, \cdot)\)	888.2.w.a	296	2
888.2.y	\(\chi_{888}(401, \cdot)\)	888.2.y.a	4	2
		888.2.y.b	16
		888.2.y.c	56
888.2.z	\(\chi_{888}(85, \cdot)\)	888.2.z.a	152	2
888.2.bd	\(\chi_{888}(491, \cdot)\)	888.2.bd.a	296	2
888.2.bf	\(\chi_{888}(455, \cdot)\)	None	0	2
888.2.bh	\(\chi_{888}(565, \cdot)\)	888.2.bh.a	152	2
888.2.bj	\(\chi_{888}(529, \cdot)\)	888.2.bj.a	8	2
		888.2.bj.b	8
		888.2.bj.c	20
888.2.bk	\(\chi_{888}(11, \cdot)\)	888.2.bk.a	296	2
888.2.bm	\(\chi_{888}(47, \cdot)\)	None	0	2
888.2.bo	\(\chi_{888}(49, \cdot)\)	888.2.bo.a	6	6
		888.2.bo.b	24
		888.2.bo.c	24
		888.2.bo.d	30
		888.2.bo.e	36
888.2.bp	\(\chi_{888}(29, \cdot)\)	888.2.bp.a	592	4
888.2.br	\(\chi_{888}(473, \cdot)\)	888.2.br.a	152	4
888.2.bu	\(\chi_{888}(547, \cdot)\)	888.2.bu.a	4	4
		888.2.bu.b	4
		888.2.bu.c	144
		888.2.bu.d	152
888.2.bw	\(\chi_{888}(103, \cdot)\)	None	0	4
888.2.by	\(\chi_{888}(71, \cdot)\)	None	0	6
888.2.cb	\(\chi_{888}(95, \cdot)\)	None	0	6
888.2.cc	\(\chi_{888}(25, \cdot)\)	888.2.cc.a	48	6
		888.2.cc.b	60
888.2.cf	\(\chi_{888}(83, \cdot)\)	888.2.cf.a	888	6
888.2.cg	\(\chi_{888}(157, \cdot)\)	888.2.cg.a	456	6
888.2.cj	\(\chi_{888}(373, \cdot)\)	888.2.cj.a	456	6
888.2.ck	\(\chi_{888}(299, \cdot)\)	888.2.ck.a	888	6
888.2.co	\(\chi_{888}(17, \cdot)\)	888.2.co.a	456	12
888.2.cp	\(\chi_{888}(55, \cdot)\)	None	0	12
888.2.cs	\(\chi_{888}(19, \cdot)\)	888.2.cs.a	456	12
		888.2.cs.b	456
888.2.ct	\(\chi_{888}(5, \cdot)\)	888.2.ct.a	1776	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 2}\)