Space of modular forms of level 243 and weight 9

• Label: 243.9
• Level: 243
• Weight: 9
• Dimension: 13728
• Nonzero newspaces: 5
• Sturm bound: 39366
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 243 = 3^{5} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 5 \)
Sturm bound:			\(39366\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(243))\).

	Total	New	Old
Modular forms	17685	13920	3765
Cusp forms	17307	13728	3579
Eisenstein series	378	192	186

Trace form

13728 * q - 36 * q^2 - 54 * q^3 - 60 * q^4 - 36 * q^5 - 54 * q^6 - 60 * q^7 - 36 * q^8 - 54 * q^9 - 84 * q^10 - 36 * q^11 - 54 * q^12 - 60 * q^13 - 36 * q^14 - 54 * q^15 + 1476 * q^16 - 36 * q^17 - 54 * q^18 - 416577 * q^19 + 677340 * q^20 - 54 * q^21 + 370884 * q^22 - 932103 * q^23 - 54 * q^24 - 1015242 * q^25 - 27 * q^26 - 54 * q^27 + 4253073 * q^28 + 2853675 * q^29 - 54 * q^30 - 1841550 * q^31 - 11467044 * q^32 - 54 * q^33 - 1321020 * q^34 + 6225381 * q^35 - 54 * q^36 + 2461353 * q^37 - 12749220 * q^38 - 54 * q^39 + 1950474 * q^40 + 6454908 * q^41 - 54 * q^42 - 8825100 * q^43 + 17341092 * q^44 - 54 * q^45 + 38733198 * q^46 + 19806732 * q^47 - 54 * q^48 - 22695036 * q^49 - 104798457 * q^50 - 54 * q^51 - 28933398 * q^52 - 27 * q^53 - 54 * q^54 + 59369217 * q^55 + 168854418 * q^56 - 54 * q^57 + 38157150 * q^58 - 7377084 * q^59 - 54 * q^60 - 68118972 * q^61 - 223709643 * q^62 - 54 * q^63 - 235185270 * q^64 + 1136502 * q^65 + 446681034 * q^66 + 302453301 * q^67 + 357443649 * q^68 - 186469722 * q^69 - 447867330 * q^70 - 628594056 * q^71 - 822804534 * q^72 - 91591752 * q^73 + 385136604 * q^74 + 369140571 * q^75 + 713561028 * q^76 + 1435552164 * q^77 + 718101450 * q^78 + 240687534 * q^79 - 81 * q^80 - 222549066 * q^81 - 839946351 * q^82 - 921643416 * q^83 - 2066577462 * q^84 - 598282560 * q^85 - 1088087076 * q^86 - 92043054 * q^87 + 599213508 * q^88 + 1652015133 * q^89 + 1693439946 * q^90 + 458031840 * q^91 + 3129096114 * q^92 + 405970758 * q^93 - 17590038 * q^94 - 640041192 * q^95 - 2774532150 * q^96 - 489702525 * q^97 - 112268061 * q^98 + 1165147092 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(243))\)

We only show spaces with odd 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
243.9.b	\(\chi_{243}(242, \cdot)\)	243.9.b.a	1	1
		243.9.b.b	1
		243.9.b.c	6
		243.9.b.d	8
		243.9.b.e	8
		243.9.b.f	8
		243.9.b.g	8
		243.9.b.h	8
		243.9.b.i	48
243.9.d	\(\chi_{243}(80, \cdot)\)	n/a	192	2
243.9.f	\(\chi_{243}(26, \cdot)\)	n/a	552	6
243.9.h	\(\chi_{243}(8, \cdot)\)	n/a	1278	18
243.9.j	\(\chi_{243}(2, \cdot)\)	n/a	11610	54

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(243))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(243)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)