Space of modular forms of level 243 and weight 5

• Label: 243.5
• Level: 243
• Weight: 5
• Dimension: 6816
• Nonzero newspaces: 5
• Sturm bound: 21870
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 243 = 3^{5} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 5 \)
Sturm bound:			\(21870\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(243))\).

	Total	New	Old
Modular forms	8937	7008	1929
Cusp forms	8559	6816	1743
Eisenstein series	378	192	186

Trace form

6816 * 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 + 36 * q^16 - 36 * q^17 - 54 * q^18 + 609 * q^19 - 900 * q^20 - 54 * q^21 - 2076 * q^22 - 3033 * q^23 - 54 * q^24 - 942 * q^25 - 27 * q^26 - 54 * q^27 + 3633 * q^28 + 3933 * q^29 - 54 * q^30 + 3270 * q^31 + 9036 * q^32 - 54 * q^33 + 612 * q^34 - 2709 * q^35 - 54 * q^36 - 4737 * q^37 - 7380 * q^38 - 54 * q^39 + 2154 * q^40 + 13356 * q^41 - 54 * q^42 + 2460 * q^43 - 4572 * q^44 - 54 * q^45 - 16338 * q^46 - 18828 * q^47 - 54 * q^48 - 11868 * q^49 - 31977 * q^50 - 54 * q^51 - 5958 * q^52 - 27 * q^53 - 54 * q^54 + 11337 * q^55 + 38754 * q^56 - 54 * q^57 + 24510 * q^58 + 30960 * q^59 - 54 * q^60 + 16644 * q^61 + 38277 * q^62 - 54 * q^63 - 45078 * q^64 - 137358 * q^65 - 96822 * q^66 - 44349 * q^67 - 90351 * q^68 + 20142 * q^69 + 36030 * q^70 + 98784 * q^71 + 207306 * q^72 + 73248 * q^73 + 241884 * q^74 + 84321 * q^75 + 101220 * q^76 + 156564 * q^77 + 65610 * q^78 + 19722 * q^79 - 81 * q^80 - 17442 * q^81 - 69231 * q^82 - 84816 * q^83 - 229878 * q^84 - 87660 * q^85 - 293796 * q^86 - 189054 * q^87 - 144732 * q^88 - 125505 * q^89 - 172854 * q^90 - 29928 * q^91 - 203886 * q^92 - 23922 * q^93 + 714 * q^94 + 34848 * q^95 + 193482 * q^96 + 50925 * q^97 + 237699 * q^98 + 167184 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(243))\)

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
243.5.b	\(\chi_{243}(242, \cdot)\)	243.5.b.a	1	1
		243.5.b.b	1
		243.5.b.c	2
		243.5.b.d	2
		243.5.b.e	2
		243.5.b.f	4
		243.5.b.g	4
		243.5.b.h	4
		243.5.b.i	4
		243.5.b.j	24
243.5.d	\(\chi_{243}(80, \cdot)\)	243.5.d.a	2	2
		243.5.d.b	2
		243.5.d.c	2
		243.5.d.d	2
		243.5.d.e	4
		243.5.d.f	4
		243.5.d.g	4
		243.5.d.h	4
		243.5.d.i	8
		243.5.d.j	8
		243.5.d.k	8
		243.5.d.l	48
243.5.f	\(\chi_{243}(26, \cdot)\)	n/a	264	6
243.5.h	\(\chi_{243}(8, \cdot)\)	n/a	630	18
243.5.j	\(\chi_{243}(2, \cdot)\)	n/a	5778	54

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(243))\) into lower level spaces

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