Space of modular forms of level 880 and weight 6

• Label: 880.6
• Level: 880
• Weight: 6
• Dimension: 58166
• Nonzero newspaces: 28
• Sturm bound: 276480
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(276480\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(880))\).

	Total	New	Old
Modular forms	116320	58654	57666
Cusp forms	114080	58166	55914
Eisenstein series	2240	488	1752

Trace form

58166 * q - 32 * q^2 - 58 * q^3 - 120 * q^4 - 99 * q^5 + 360 * q^6 + 430 * q^7 + 952 * q^8 + 230 * q^9 - 916 * q^10 - 2618 * q^11 - 48 * q^12 + 690 * q^13 - 424 * q^14 + 2079 * q^15 - 3576 * q^16 - 870 * q^17 - 12576 * q^18 - 16326 * q^19 + 5900 * q^20 + 10700 * q^21 + 8808 * q^22 + 7976 * q^23 + 33448 * q^24 - 20691 * q^25 + 29384 * q^26 - 2278 * q^27 - 45752 * q^28 - 16378 * q^29 - 71876 * q^30 - 26002 * q^31 + 6328 * q^32 + 77694 * q^33 + 91408 * q^34 - 14003 * q^35 - 24360 * q^36 - 131038 * q^37 + 63896 * q^38 - 118414 * q^39 - 86460 * q^40 + 52618 * q^41 + 19816 * q^42 + 133224 * q^43 - 38896 * q^44 + 203146 * q^45 - 82856 * q^46 + 228394 * q^47 - 233720 * q^48 - 212898 * q^49 - 76924 * q^50 - 427546 * q^51 + 52600 * q^52 - 138734 * q^53 + 710248 * q^54 - 10859 * q^55 + 764304 * q^56 + 695502 * q^57 + 427080 * q^58 + 94842 * q^59 - 292396 * q^60 - 309158 * q^61 - 1095512 * q^62 - 321488 * q^63 - 582120 * q^64 - 191918 * q^65 - 341696 * q^66 - 85120 * q^67 - 72104 * q^68 + 305332 * q^69 - 310920 * q^70 + 478522 * q^71 - 280608 * q^72 + 135538 * q^73 + 1381744 * q^74 + 201207 * q^75 + 2431800 * q^76 + 1041558 * q^77 + 2279328 * q^78 - 847154 * q^79 + 527784 * q^80 - 172994 * q^81 - 118440 * q^82 - 368942 * q^83 - 1153768 * q^84 - 1173191 * q^85 - 766856 * q^86 + 290256 * q^87 - 4230168 * q^88 - 1043220 * q^89 - 3663020 * q^90 - 368170 * q^91 - 2989608 * q^92 + 452222 * q^93 - 1051560 * q^94 + 137369 * q^95 + 1847640 * q^96 + 2399538 * q^97 + 4559208 * q^98 + 341766 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(880))\)

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
880.6.a	\(\chi_{880}(1, \cdot)\)	880.6.a.a	1	1
		880.6.a.b	1
		880.6.a.c	1
		880.6.a.d	1
		880.6.a.e	1
		880.6.a.f	2
		880.6.a.g	2
		880.6.a.h	2
		880.6.a.i	3
		880.6.a.j	3
		880.6.a.k	3
		880.6.a.l	3
		880.6.a.m	4
		880.6.a.n	4
		880.6.a.o	4
		880.6.a.p	5
		880.6.a.q	5
		880.6.a.r	5
		880.6.a.s	5
		880.6.a.t	6
		880.6.a.u	6
		880.6.a.v	6
		880.6.a.w	6
		880.6.a.x	7
		880.6.a.y	7
		880.6.a.z	7
880.6.b	\(\chi_{880}(529, \cdot)\)	n/a	150	1
880.6.c	\(\chi_{880}(439, \cdot)\)	None	0	1
880.6.f	\(\chi_{880}(351, \cdot)\)	n/a	120	1
880.6.g	\(\chi_{880}(441, \cdot)\)	None	0	1
880.6.l	\(\chi_{880}(89, \cdot)\)	None	0	1
880.6.m	\(\chi_{880}(879, \cdot)\)	n/a	180	1
880.6.p	\(\chi_{880}(791, \cdot)\)	None	0	1
880.6.s	\(\chi_{880}(67, \cdot)\)	n/a	1200	2
880.6.t	\(\chi_{880}(197, \cdot)\)	n/a	1432	2
880.6.v	\(\chi_{880}(131, \cdot)\)	n/a	960	2
880.6.w	\(\chi_{880}(221, \cdot)\)	n/a	800	2
880.6.z	\(\chi_{880}(23, \cdot)\)	None	0	2
880.6.bb	\(\chi_{880}(153, \cdot)\)	None	0	2
880.6.bd	\(\chi_{880}(417, \cdot)\)	n/a	356	2
880.6.bf	\(\chi_{880}(287, \cdot)\)	n/a	300	2
880.6.bh	\(\chi_{880}(309, \cdot)\)	n/a	1200	2
880.6.bi	\(\chi_{880}(219, \cdot)\)	n/a	1432	2
880.6.bk	\(\chi_{880}(243, \cdot)\)	n/a	1200	2
880.6.bl	\(\chi_{880}(373, \cdot)\)	n/a	1432	2
880.6.bo	\(\chi_{880}(81, \cdot)\)	n/a	480	4
880.6.bp	\(\chi_{880}(151, \cdot)\)	None	0	4
880.6.bs	\(\chi_{880}(79, \cdot)\)	n/a	720	4
880.6.bt	\(\chi_{880}(9, \cdot)\)	None	0	4
880.6.by	\(\chi_{880}(201, \cdot)\)	None	0	4
880.6.bz	\(\chi_{880}(271, \cdot)\)	n/a	480	4
880.6.cc	\(\chi_{880}(39, \cdot)\)	None	0	4
880.6.cd	\(\chi_{880}(49, \cdot)\)	n/a	712	4
880.6.cg	\(\chi_{880}(237, \cdot)\)	n/a	5728	8
880.6.ch	\(\chi_{880}(3, \cdot)\)	n/a	5728	8
880.6.ci	\(\chi_{880}(19, \cdot)\)	n/a	5728	8
880.6.cl	\(\chi_{880}(69, \cdot)\)	n/a	5728	8
880.6.cm	\(\chi_{880}(17, \cdot)\)	n/a	1424	8
880.6.co	\(\chi_{880}(47, \cdot)\)	n/a	1440	8
880.6.cq	\(\chi_{880}(103, \cdot)\)	None	0	8
880.6.cs	\(\chi_{880}(57, \cdot)\)	None	0	8
880.6.cu	\(\chi_{880}(141, \cdot)\)	n/a	3840	8
880.6.cx	\(\chi_{880}(51, \cdot)\)	n/a	3840	8
880.6.cy	\(\chi_{880}(13, \cdot)\)	n/a	5728	8
880.6.cz	\(\chi_{880}(147, \cdot)\)	n/a	5728	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(880))\) into lower level spaces

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