Space of modular forms of level 880 and weight 2

• Label: 880.2
• Level: 880
• Weight: 2
• Dimension: 11438
• Nonzero newspaces: 28
• Newform subspaces: 106
• Sturm bound: 92160
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Newform subspaces:			\( 106 \)
Sturm bound:			\(92160\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(880))\).

	Total	New	Old
Modular forms	24160	11926	12234
Cusp forms	21921	11438	10483
Eisenstein series	2239	488	1751

Trace form

11438 * q - 32 * q^2 - 26 * q^3 - 24 * q^4 - 59 * q^5 - 72 * q^6 - 18 * q^7 - 8 * q^8 - 2 * q^9 - 44 * q^10 - 74 * q^11 - 80 * q^12 - 30 * q^13 - 40 * q^14 - q^15 - 120 * q^16 - 54 * q^17 - 16 * q^18 + 26 * q^19 - 36 * q^20 - 52 * q^21 - 32 * q^22 - 24 * q^23 - 24 * q^24 + 5 * q^25 - 72 * q^26 - 38 * q^27 - 56 * q^28 - 10 * q^29 - 116 * q^30 - 146 * q^31 - 72 * q^32 - 66 * q^33 - 176 * q^34 - 35 * q^35 - 232 * q^36 - 46 * q^37 - 184 * q^38 + 50 * q^39 - 220 * q^40 - 6 * q^41 - 184 * q^42 + 40 * q^43 - 96 * q^44 - 126 * q^45 - 168 * q^46 + 106 * q^47 - 120 * q^48 + 22 * q^49 - 156 * q^50 + 102 * q^51 - 104 * q^52 + 2 * q^53 - 120 * q^54 + 5 * q^55 - 240 * q^56 + 110 * q^57 - 72 * q^58 + 26 * q^59 + 20 * q^60 - 150 * q^61 + 40 * q^62 - 112 * q^63 + 24 * q^64 - 30 * q^65 - 32 * q^66 - 160 * q^67 + 88 * q^68 - 44 * q^69 - 24 * q^70 - 198 * q^71 + 32 * q^72 - 126 * q^73 - 48 * q^74 - 297 * q^75 - 232 * q^76 - 202 * q^77 - 288 * q^78 - 306 * q^79 - 88 * q^80 - 394 * q^81 - 296 * q^82 - 302 * q^83 - 232 * q^84 - 215 * q^85 - 280 * q^86 - 432 * q^87 - 568 * q^88 - 132 * q^89 - 132 * q^90 - 234 * q^91 - 360 * q^92 - 258 * q^93 - 456 * q^94 - 199 * q^95 - 424 * q^96 - 254 * q^97 - 552 * q^98 - 202 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)

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
880.2.a	\(\chi_{880}(1, \cdot)\)	880.2.a.a	1	1
		880.2.a.b	1
		880.2.a.c	1
		880.2.a.d	1
		880.2.a.e	1
		880.2.a.f	1
		880.2.a.g	1
		880.2.a.h	1
		880.2.a.i	1
		880.2.a.j	1
		880.2.a.k	2
		880.2.a.l	2
		880.2.a.m	2
		880.2.a.n	2
		880.2.a.o	2
880.2.b	\(\chi_{880}(529, \cdot)\)	880.2.b.a	2	1
		880.2.b.b	2
		880.2.b.c	2
		880.2.b.d	2
		880.2.b.e	2
		880.2.b.f	2
		880.2.b.g	2
		880.2.b.h	4
		880.2.b.i	4
		880.2.b.j	8
880.2.c	\(\chi_{880}(439, \cdot)\)	None	0	1
880.2.f	\(\chi_{880}(351, \cdot)\)	880.2.f.a	2	1
		880.2.f.b	2
		880.2.f.c	4
		880.2.f.d	8
		880.2.f.e	8
880.2.g	\(\chi_{880}(441, \cdot)\)	None	0	1
880.2.l	\(\chi_{880}(89, \cdot)\)	None	0	1
880.2.m	\(\chi_{880}(879, \cdot)\)	880.2.m.a	2	1
		880.2.m.b	2
		880.2.m.c	4
		880.2.m.d	4
		880.2.m.e	8
		880.2.m.f	8
		880.2.m.g	8
880.2.p	\(\chi_{880}(791, \cdot)\)	None	0	1
880.2.s	\(\chi_{880}(67, \cdot)\)	880.2.s.a	4	2
		880.2.s.b	236
880.2.t	\(\chi_{880}(197, \cdot)\)	880.2.t.a	8	2
		880.2.t.b	272
880.2.v	\(\chi_{880}(131, \cdot)\)	880.2.v.a	192	2
880.2.w	\(\chi_{880}(221, \cdot)\)	880.2.w.a	72	2
		880.2.w.b	88
880.2.z	\(\chi_{880}(23, \cdot)\)	None	0	2
880.2.bb	\(\chi_{880}(153, \cdot)\)	None	0	2
880.2.bd	\(\chi_{880}(417, \cdot)\)	880.2.bd.a	4	2
		880.2.bd.b	4
		880.2.bd.c	4
		880.2.bd.d	4
		880.2.bd.e	4
		880.2.bd.f	4
		880.2.bd.g	4
		880.2.bd.h	8
		880.2.bd.i	32
880.2.bf	\(\chi_{880}(287, \cdot)\)	880.2.bf.a	2	2
		880.2.bf.b	2
		880.2.bf.c	2
		880.2.bf.d	2
		880.2.bf.e	6
		880.2.bf.f	6
		880.2.bf.g	20
		880.2.bf.h	20
880.2.bh	\(\chi_{880}(309, \cdot)\)	880.2.bh.a	240	2
880.2.bi	\(\chi_{880}(219, \cdot)\)	880.2.bi.a	4	2
		880.2.bi.b	4
		880.2.bi.c	16
		880.2.bi.d	256
880.2.bk	\(\chi_{880}(243, \cdot)\)	880.2.bk.a	4	2
		880.2.bk.b	236
880.2.bl	\(\chi_{880}(373, \cdot)\)	880.2.bl.a	8	2
		880.2.bl.b	272
880.2.bo	\(\chi_{880}(81, \cdot)\)	880.2.bo.a	4	4
		880.2.bo.b	4
		880.2.bo.c	8
		880.2.bo.d	8
		880.2.bo.e	8
		880.2.bo.f	8
		880.2.bo.g	8
		880.2.bo.h	8
		880.2.bo.i	12
		880.2.bo.j	12
		880.2.bo.k	16
880.2.bp	\(\chi_{880}(151, \cdot)\)	None	0	4
880.2.bs	\(\chi_{880}(79, \cdot)\)	880.2.bs.a	48	4
		880.2.bs.b	96
880.2.bt	\(\chi_{880}(9, \cdot)\)	None	0	4
880.2.by	\(\chi_{880}(201, \cdot)\)	None	0	4
880.2.bz	\(\chi_{880}(271, \cdot)\)	880.2.bz.a	16	4
		880.2.bz.b	16
		880.2.bz.c	32
		880.2.bz.d	32
880.2.cc	\(\chi_{880}(39, \cdot)\)	None	0	4
880.2.cd	\(\chi_{880}(49, \cdot)\)	880.2.cd.a	8	4
		880.2.cd.b	16
		880.2.cd.c	16
		880.2.cd.d	24
		880.2.cd.e	72
880.2.cg	\(\chi_{880}(237, \cdot)\)	880.2.cg.a	1120	8
880.2.ch	\(\chi_{880}(3, \cdot)\)	880.2.ch.a	1120	8
880.2.ci	\(\chi_{880}(19, \cdot)\)	880.2.ci.a	1120	8
880.2.cl	\(\chi_{880}(69, \cdot)\)	880.2.cl.a	1120	8
880.2.cm	\(\chi_{880}(17, \cdot)\)	880.2.cm.a	32	8
		880.2.cm.b	48
		880.2.cm.c	48
		880.2.cm.d	144
880.2.co	\(\chi_{880}(47, \cdot)\)	880.2.co.a	96	8
		880.2.co.b	192
880.2.cq	\(\chi_{880}(103, \cdot)\)	None	0	8
880.2.cs	\(\chi_{880}(57, \cdot)\)	None	0	8
880.2.cu	\(\chi_{880}(141, \cdot)\)	880.2.cu.a	768	8
880.2.cx	\(\chi_{880}(51, \cdot)\)	880.2.cx.a	768	8
880.2.cy	\(\chi_{880}(13, \cdot)\)	880.2.cy.a	1120	8
880.2.cz	\(\chi_{880}(147, \cdot)\)	880.2.cz.a	1120	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)