Space of modular forms of level 729, weight 6, and Character 729.i

• Label: 729.6.i
• Level: $729$
• Weight: $6$
• Character orbit: 729.i
• Rep. character: $\chi_{729}(10,\cdot)$
• Character field: $\Q(\zeta_{81})$
• Dimension: $7236$
• Sturm bound: $486$

Defining parameters

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\) and degree \(54\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 243 \)
Character field:			\(\Q(\zeta_{81})\)
Sturm bound:			\(486\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(729, [\chi])\).

	Total	New	Old
Modular forms	22032	7344	14688
Cusp forms	21708	7236	14472
Eisenstein series	324	108	216

Trace form

7236 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 592596 * q^65 - 54 * q^67 + 759078 * q^68 - 54 * q^70 + 610362 * q^71 - 54 * q^73 + 263574 * q^74 - 54 * q^76 - 849042 * q^77 - 54 * q^79 - 2419173 * q^80 - 27 * q^82 - 510678 * q^83 - 54 * q^85 + 128790 * q^86 - 54 * q^88 + 964629 * q^89 - 54 * q^91 + 3416310 * q^92 - 54 * q^94 + 483354 * q^95 - 54 * q^97 - 2086938 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(729, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(729, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(729, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 2}\)