Space of modular forms of level 243 and weight 4

• Label: 243.4
• Level: 243
• Weight: 4
• Dimension: 5088
• Nonzero newspaces: 5
• Newform subspaces: 28
• Sturm bound: 17496
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 243 = 3^{5} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(17496\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(243))\).

	Total	New	Old
Modular forms	6750	5280	1470
Cusp forms	6372	5088	1284
Eisenstein series	378	192	186

Trace form

5088 * 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 - 108 * q^16 - 36 * q^17 - 54 * q^18 - 354 * q^19 - 612 * q^20 - 54 * q^21 + 48 * q^22 + 342 * q^23 - 54 * q^24 + 372 * q^25 + 1359 * q^26 - 54 * q^27 + 753 * q^28 + 504 * q^29 - 54 * q^30 + 48 * q^31 - 252 * q^32 - 54 * q^33 - 648 * q^34 - 1278 * q^35 - 54 * q^36 - 840 * q^37 - 990 * q^38 - 54 * q^39 - 1194 * q^40 - 1890 * q^41 - 54 * q^42 - 1086 * q^43 - 2700 * q^44 - 54 * q^45 - 246 * q^46 + 558 * q^47 - 54 * q^48 + 1128 * q^49 + 4761 * q^50 - 54 * q^51 + 2862 * q^52 + 2817 * q^53 - 54 * q^54 + 2643 * q^55 + 5814 * q^56 - 54 * q^57 + 1722 * q^58 + 1413 * q^59 - 54 * q^60 - 168 * q^61 - 1917 * q^62 - 54 * q^63 + 2982 * q^64 + 10098 * q^65 + 13986 * q^66 + 4044 * q^67 + 16839 * q^68 + 5562 * q^69 + 1614 * q^70 + 1764 * q^71 - 2646 * q^72 - 2676 * q^73 - 13716 * q^74 - 6804 * q^75 - 11784 * q^76 - 24516 * q^77 - 16038 * q^78 - 9888 * q^79 - 50391 * q^80 - 8694 * q^81 - 16959 * q^82 - 13356 * q^83 - 25758 * q^84 - 8370 * q^85 - 18036 * q^86 - 8262 * q^87 - 7716 * q^88 - 8181 * q^89 + 2106 * q^90 - 2784 * q^91 + 16074 * q^92 + 8154 * q^93 + 8742 * q^94 + 18072 * q^95 + 30186 * q^96 + 11874 * q^97 + 43551 * q^98 + 14094 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(243))\)

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
243.4.a	\(\chi_{243}(1, \cdot)\)	243.4.a.a	1	1
		243.4.a.b	1
		243.4.a.c	1
		243.4.a.d	1
		243.4.a.e	2
		243.4.a.f	2
		243.4.a.g	2
		243.4.a.h	4
		243.4.a.i	4
		243.4.a.j	9
		243.4.a.k	9
243.4.c	\(\chi_{243}(82, \cdot)\)	243.4.c.a	2	2
		243.4.c.b	2
		243.4.c.c	2
		243.4.c.d	2
		243.4.c.e	4
		243.4.c.f	4
		243.4.c.g	4
		243.4.c.h	8
		243.4.c.i	8
		243.4.c.j	18
		243.4.c.k	18
243.4.e	\(\chi_{243}(28, \cdot)\)	243.4.e.a	48	6
		243.4.e.b	48
		243.4.e.c	48
		243.4.e.d	48
243.4.g	\(\chi_{243}(10, \cdot)\)	243.4.g.a	468	18
243.4.i	\(\chi_{243}(4, \cdot)\)	243.4.i.a	4320	54

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(243))\) into lower level spaces

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