Space of modular forms of level 1089 and weight 6

• Label: 1089.6
• Level: 1089
• Weight: 6
• Dimension: 168954
• Nonzero newspaces: 16
• Sturm bound: 522720
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(522720\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1089))\).

	Total	New	Old
Modular forms	219080	170219	48861
Cusp forms	216520	168954	47566
Eisenstein series	2560	1265	1295

Trace form

168954 * q - 126 * q^2 - 192 * q^3 - 180 * q^4 - 63 * q^5 - 9 * q^6 - 737 * q^7 - 1373 * q^8 - 594 * q^9 + 1629 * q^10 + 295 * q^11 + 2384 * q^12 - 689 * q^13 + 2007 * q^14 - 2232 * q^15 - 17840 * q^16 - 8883 * q^17 - 8280 * q^18 + 4461 * q^19 + 22615 * q^20 + 8490 * q^21 + 12420 * q^22 - 30221 * q^23 - 3471 * q^24 + 21302 * q^25 + 46675 * q^26 + 29928 * q^27 + 6001 * q^28 - 17885 * q^29 - 44796 * q^30 - 13523 * q^31 - 126962 * q^32 - 49750 * q^33 - 108902 * q^34 - 126229 * q^35 + 9871 * q^36 - 24371 * q^37 + 191854 * q^38 + 116700 * q^39 + 401567 * q^40 + 235173 * q^41 + 76158 * q^42 + 42147 * q^43 - 127135 * q^44 - 112722 * q^45 + 12965 * q^46 - 42133 * q^47 - 78065 * q^48 - 134402 * q^49 - 326666 * q^50 - 230156 * q^51 - 619083 * q^52 - 134923 * q^53 + 335201 * q^54 + 265290 * q^55 + 1449195 * q^56 + 471362 * q^57 + 858275 * q^58 + 345405 * q^59 + 165128 * q^60 - 20205 * q^61 - 787401 * q^62 - 383296 * q^63 - 1921339 * q^64 - 1314879 * q^65 - 540870 * q^66 - 1050901 * q^67 - 1384582 * q^68 - 398962 * q^69 + 321401 * q^70 + 586317 * q^71 + 934971 * q^72 + 784287 * q^73 + 2332095 * q^74 + 943588 * q^75 + 1673040 * q^76 + 662085 * q^77 + 1161282 * q^78 - 179761 * q^79 + 344343 * q^80 + 991662 * q^81 - 3240003 * q^82 - 537781 * q^83 - 1482366 * q^84 + 725023 * q^85 - 1786466 * q^86 - 2017336 * q^87 + 571930 * q^88 - 1190327 * q^89 - 2573672 * q^90 + 1491377 * q^91 + 963109 * q^92 + 573518 * q^93 - 133509 * q^94 + 1383879 * q^95 + 5208928 * q^96 - 1768017 * q^97 + 67007 * q^98 + 1520600 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1089))\)

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
1089.6.a	\(\chi_{1089}(1, \cdot)\)	1089.6.a.a	1	1
		1089.6.a.b	1
		1089.6.a.c	1
		1089.6.a.d	1
		1089.6.a.e	1
		1089.6.a.f	1
		1089.6.a.g	1
		1089.6.a.h	1
		1089.6.a.i	1
		1089.6.a.j	2
		1089.6.a.k	2
		1089.6.a.l	2
		1089.6.a.m	2
		1089.6.a.n	2
		1089.6.a.o	2
		1089.6.a.p	2
		1089.6.a.q	3
		1089.6.a.r	3
		1089.6.a.s	3
		1089.6.a.t	4
		1089.6.a.u	4
		1089.6.a.v	5
		1089.6.a.w	5
		1089.6.a.x	5
		1089.6.a.y	5
		1089.6.a.z	6
		1089.6.a.ba	6
		1089.6.a.bb	8
		1089.6.a.bc	8
		1089.6.a.bd	8
		1089.6.a.be	8
		1089.6.a.bf	8
		1089.6.a.bg	8
		1089.6.a.bh	10
		1089.6.a.bi	10
		1089.6.a.bj	10
		1089.6.a.bk	10
		1089.6.a.bl	10
		1089.6.a.bm	12
		1089.6.a.bn	20
		1089.6.a.bo	20
1089.6.d	\(\chi_{1089}(1088, \cdot)\)	n/a	180	1
1089.6.e	\(\chi_{1089}(364, \cdot)\)	n/a	1072	2
1089.6.f	\(\chi_{1089}(487, \cdot)\)	n/a	884	4
1089.6.g	\(\chi_{1089}(362, \cdot)\)	n/a	1064	2
1089.6.j	\(\chi_{1089}(161, \cdot)\)	n/a	720	4
1089.6.m	\(\chi_{1089}(100, \cdot)\)	n/a	2740	10
1089.6.n	\(\chi_{1089}(124, \cdot)\)	n/a	4256	8
1089.6.o	\(\chi_{1089}(98, \cdot)\)	n/a	2200	10
1089.6.t	\(\chi_{1089}(239, \cdot)\)	n/a	4256	8
1089.6.u	\(\chi_{1089}(34, \cdot)\)	n/a	13160	20
1089.6.v	\(\chi_{1089}(37, \cdot)\)	n/a	10960	40
1089.6.y	\(\chi_{1089}(32, \cdot)\)	n/a	13160	20
1089.6.bb	\(\chi_{1089}(8, \cdot)\)	n/a	8800	40
1089.6.bc	\(\chi_{1089}(4, \cdot)\)	n/a	52640	80
1089.6.bd	\(\chi_{1089}(2, \cdot)\)	n/a	52640	80

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1089))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1089)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 1}\)