Space of modular forms of level 243 and weight 2

• Label: 243.2
• Level: 243
• Weight: 2
• Dimension: 1632
• Nonzero newspaces: 5
• Newform subspaces: 18
• Sturm bound: 8748
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 243 = 3^{5} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(8748\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(243))\).

	Total	New	Old
Modular forms	2376	1824	552
Cusp forms	1999	1632	367
Eisenstein series	377	192	185

Trace form

1632 * 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 - 72 * q^16 - 36 * q^17 - 54 * q^18 - 93 * q^19 - 72 * q^20 - 54 * q^21 - 78 * q^22 - 63 * q^23 - 54 * q^24 - 78 * q^25 - 99 * q^26 - 54 * q^27 - 147 * q^28 - 63 * q^29 - 54 * q^30 - 78 * q^31 - 90 * q^32 - 54 * q^33 - 90 * q^34 - 63 * q^35 - 54 * q^36 - 93 * q^37 - 45 * q^38 - 54 * q^39 - 114 * q^40 - 54 * q^41 - 54 * q^42 - 78 * q^43 - 108 * q^44 - 54 * q^45 - 138 * q^46 - 90 * q^47 - 54 * q^48 - 96 * q^49 - 153 * q^50 - 54 * q^51 - 72 * q^52 - 99 * q^53 - 54 * q^54 - 165 * q^55 - 180 * q^56 - 54 * q^57 - 114 * q^58 - 99 * q^59 - 54 * q^60 - 96 * q^61 - 135 * q^62 - 54 * q^63 - 42 * q^64 + 54 * q^66 - 15 * q^67 + 234 * q^68 + 54 * q^69 + 12 * q^70 + 144 * q^71 + 270 * q^72 + 24 * q^73 + 324 * q^74 + 81 * q^75 + 105 * q^76 + 324 * q^77 + 162 * q^78 + 66 * q^79 + 639 * q^80 + 54 * q^81 + 105 * q^82 + 144 * q^83 + 324 * q^84 + 36 * q^85 + 324 * q^86 + 162 * q^87 + 69 * q^88 + 162 * q^89 + 162 * q^90 - 12 * q^91 + 414 * q^92 + 54 * q^93 + 12 * q^94 + 36 * q^95 + 135 * q^96 - 51 * q^97 - 27 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)

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
243.2.a	\(\chi_{243}(1, \cdot)\)	243.2.a.a	1	1
		243.2.a.b	1
		243.2.a.c	2
		243.2.a.d	2
		243.2.a.e	3
		243.2.a.f	3
243.2.c	\(\chi_{243}(82, \cdot)\)	243.2.c.a	2	2
		243.2.c.b	2
		243.2.c.c	4
		243.2.c.d	4
		243.2.c.e	6
		243.2.c.f	6
243.2.e	\(\chi_{243}(28, \cdot)\)	243.2.e.a	12	6
		243.2.e.b	12
		243.2.e.c	12
		243.2.e.d	12
243.2.g	\(\chi_{243}(10, \cdot)\)	243.2.g.a	144	18
243.2.i	\(\chi_{243}(4, \cdot)\)	243.2.i.a	1404	54

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(243))\) into lower level spaces

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