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Properties

Label 243.3.h
Level $243$
Weight $3$
Character orbit 243.h
Rep. character $\chi_{243}(8,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $306$
Newform subspaces $1$
Sturm bound $81$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 243.h (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Newform subspaces: \( 1 \)
Sturm bound: \(81\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(243, [\chi])\).

Total New Old
Modular forms 1026 342 684
Cusp forms 918 306 612
Eisenstein series 108 36 72

Trace form

\( 306 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} + 234 q^{20} - 18 q^{22} + 99 q^{23} - 18 q^{25} + 27 q^{26}+ \cdots + 2853 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(243, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
243.3.h.a 243.h 81.h $306$ $6.621$ None 81.3.h.a \(18\) \(0\) \(18\) \(-18\) $\mathrm{SU}(2)[C_{54}]$

Decomposition of \(S_{3}^{\mathrm{old}}(243, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(243, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)