Space of modular forms of level 1089, weight 6, and Character 1089.t

• Label: 1089.6.t
• Level: $1089$
• Weight: $6$
• Character orbit: 1089.t
• Rep. character: $\chi_{1089}(239,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $4256$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1089.t (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1089, [\chi])\).

	Total	New	Old
Modular forms	5376	4384	992
Cusp forms	5184	4256	928
Eisenstein series	192	128	64

Trace form

\( 4256 q + 15 q^{2} + 26 q^{3} + 8387 q^{4} + 183 q^{5} + 30 q^{6} + 5 q^{7} - 658 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)