Space of modular forms of level 243, weight 6, and Character 243.i

• Label: 243.6.i
• Level: $243$
• Weight: $6$
• Character orbit: 243.i
• Rep. character: $\chi_{243}(4,\cdot)$
• Character field: $\Q(\zeta_{81})$
• Dimension: $7236$
• Sturm bound: $162$

Defining parameters

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\) and degree \(54\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 243 \)
Character field:			\(\Q(\zeta_{81})\)
Sturm bound:			\(162\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(243, [\chi])\).

	Total	New	Old
Modular forms	7344	7344	0
Cusp forms	7236	7236	0
Eisenstein series	108	108	0

Trace form

7236 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 592596 * q^65 + 428058 * q^66 - 54 * q^67 - 759078 * q^68 - 609714 * q^69 - 54 * q^70 - 610362 * q^71 - 1472310 * q^72 - 54 * q^73 - 263574 * q^74 + 84321 * q^75 - 54 * q^76 + 849042 * q^77 + 1115370 * q^78 - 54 * q^79 + 2419173 * q^80 + 682398 * q^81 - 27 * q^82 + 510678 * q^83 + 1239786 * q^84 - 54 * q^85 - 128790 * q^86 - 608958 * q^87 - 54 * q^88 - 964629 * q^89 - 1922454 * q^90 - 54 * q^91 - 3416310 * q^92 - 1073682 * q^93 - 54 * q^94 - 483354 * q^95 + 193482 * q^96 - 54 * q^97 + 2086938 * q^98 + 1776816 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(243, [\chi])\) into newform subspaces

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