Space of modular forms of level 729 and weight 6

• Label: 729.6
• Level: 729
• Weight: 6
• Dimension: 77436
• Nonzero newspaces: 6
• Sturm bound: 236196
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 729 = 3^{6} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(236196\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(729))\).

	Total	New	Old
Modular forms	99063	78084	20979
Cusp forms	97767	77436	20331
Eisenstein series	1296	648	648

Trace form

77436 * q - 108 * q^2 - 162 * q^3 - 180 * q^4 - 108 * q^5 - 162 * q^6 - 180 * q^7 - 108 * q^8 - 162 * q^9 - 252 * q^10 - 108 * q^11 - 162 * q^12 - 180 * q^13 - 108 * q^14 - 162 * q^15 - 180 * q^16 - 108 * q^17 - 162 * q^18 - 252 * q^19 - 108 * q^20 - 162 * q^21 - 180 * q^22 - 108 * q^23 - 162 * q^24 - 180 * q^25 - 108 * q^26 - 162 * q^27 - 324 * q^28 - 108 * q^29 - 162 * q^30 - 180 * q^31 - 108 * q^32 - 162 * q^33 - 180 * q^34 - 108 * q^35 - 162 * q^36 - 252 * q^37 - 108 * q^38 - 162 * q^39 - 180 * q^40 - 108 * q^41 - 162 * q^42 - 180 * q^43 - 108 * q^44 - 162 * q^45 - 252 * q^46 - 108 * q^47 - 162 * q^48 - 180 * q^49 - 108 * q^50 - 162 * q^51 - 756 * q^52 - 108 * q^53 - 162 * q^54 - 324 * q^55 - 108 * q^56 - 162 * q^57 - 180 * q^58 - 108 * q^59 - 162 * q^60 - 180 * q^61 - 108 * q^62 - 162 * q^63 - 295164 * q^64 - 592758 * q^65 - 162 * q^66 + 49446 * q^67 + 758916 * q^68 - 162 * q^69 + 658620 * q^70 + 610200 * q^71 - 162 * q^72 + 242829 * q^73 + 263412 * q^74 - 162 * q^75 - 386388 * q^76 - 849204 * q^77 - 162 * q^78 - 648720 * q^79 - 2419335 * q^80 - 162 * q^81 - 932877 * q^82 - 510840 * q^83 - 162 * q^84 - 159480 * q^85 + 128628 * q^86 - 162 * q^87 + 818892 * q^88 + 964467 * q^89 - 162 * q^90 + 818739 * q^91 + 3416148 * q^92 - 162 * q^93 + 865980 * q^94 + 483192 * q^95 - 162 * q^96 - 477054 * q^97 - 2087100 * q^98 - 162 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(729))\)

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
729.6.a	\(\chi_{729}(1, \cdot)\)	729.6.a.a	24	1
		729.6.a.b	24
		729.6.a.c	42
		729.6.a.d	42
		729.6.a.e	42
729.6.c	\(\chi_{729}(244, \cdot)\)	n/a	348	2
729.6.e	\(\chi_{729}(82, \cdot)\)	n/a	1062	6
729.6.g	\(\chi_{729}(28, \cdot)\)	n/a	3168	18
729.6.i	\(\chi_{729}(10, \cdot)\)	n/a	7236	54
729.6.k	\(\chi_{729}(4, \cdot)\)	n/a	65448	162

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(729))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(729)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)